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Mathematic Quiz

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1) Evaluate $2.9999^{2}$

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2) My watch is 1 minute slow at 1.00 pm on Tuesday and 2 minutes fast at 1.00 pm on Thursday. When did it show the correct time?

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3) A can give B a 30 meters start and C an 80 meters start in a kilometer race. What start can B give to C in the same race?
(1 Kilometer = 1000 meters)

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4) How much will $12,000 amount to in 2 years at compound interest if the rates for the 2 years are 5% and 7% per annum? 5 / 200 5) Find the distance between points P (-3, 2) and Q (-5, 8). 6 / 200 6) What is the Geometric mean of 24, 27 and 72? 7 / 200 7) Find the fraction such that if numerator is multiplied by 2 and 2 is added to the denominator, the fraction equals 2. If the numerator is squared and 2 is added to the denominator, the fraction equals 7. 8 / 200 8) Simplify 1/[1+1/{1+1/(1+1/4)}] 9 / 200 9) If a man walks to his office at 3/4th of his usual rate, he reaches office 1/3rd of an hour later than usual. How much time does he usually take to reach his office? 10 / 200 10) In how much time will a tank be filled by 4 pipes of diameter 1 cm, 2 cms, 3 cms and 6 cms running into it simultaneously? Given that the largest pipe alone fills it in 36 minutes. 11 / 200 11) What is the annual rate of growth of population of bacteria which has increased by 25% in the first hour 30% in the second hour and 10% in the third hour? 12 / 200 12) The coordinates of P, Q and R are $\left( \cfrac{2}{3},\cfrac{3}{2} \right)$, (1, –3) and (x, y) respectively. If R is the midpoint of PQ, find the values of x and y. 13 / 200 13) In a class of 80 students, there are 50 girls and 30 boys. The average weight of the class is 50 lbs. If the average weight of boys is 55 lbs, what is the average weight of girls? 14 / 200 14) If $x-y=3$ and $x^{3}-y^{3}=189$; $x+y$ =? 15 / 200 15) Reduce the Expression: $\cfrac{4.5x^{3}\times 15}{\sqrt{y}(x+y)^{2}}$ = $\cfrac{3^{3}\times 5\sqrt{4y}}{2x^{2}y+4xy^{2}+2y^{3}}$ 16 / 200 16) A and B have to go from X to Y which are at a distance of 230 kms from each other. A drives at a constant speed of 100 kms/hr for the first 115 kms and then at an average speed of 50 kms/hr for the remaining distance. B starts with an initial speed of 50 kms/hr at X and drives with constant acceleration such that when he reaches Y, his speed is 100 kms/hr. Which of the following statements is true? 17 / 200 17) In an alloy of three metals A, B and C, the quantity of metal A is 4/5th of B and that of B is 3/4th of C. What is the quantity in lb of each metal in 47 lbs of the alloy? (In the order of A, B and C.) 18 / 200 18)$2000 @ 5% compound interest after 4 years will become…?

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19) Find the coordinates of point B if B divides A and C internally in the ratio of 2 : 3. Given that A (–3, –4) and C (2, –1).

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20) In an exam, the average marks obtained by a student in English, Algebra, Geometry and Drawing were 50. His average marks in Algebra, Science, Social Studies and Craft were 70. If the average marks in all 7 subjects were 58. What is his Algebra score?

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21) Find the value of ‘1’ in $2^{4a+4}=4^{2a+1}+12$.

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22) Find the HCF and LCM of $6a^{2}b^{3}$, $9a^{5}b$ and $12a^{2}bc^{2}$

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23) If I walk at 3 mph (miles per hour), I miss the train by 2 minutes. If however, I walk at 4 mph, I reach the station 2 minutes before arrival of the train. How far do I walk to reach the station?

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24) 3 men and 6 women can dig a well in 4 days. 5 men and 4 women take 3 days. How many days would 8 women and 1 man take?

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25) Find the ratio in which the point X $\left( \cfrac{4}{3},4 \right)$ divides the line A (3, 5) and B (–2, 2).

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26) In a class of 40, there are 10 boys at the age of 12 years, 12 at the age of 12.5 and the rest at the age of 13. The average age of all boys in the class is ___________ years.

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27) On dividing a number by 1005 the quotient is 785 and the remainder is 108. What is the number?

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28) If $x*y$ means $y(x-y)$; find the value of 3.124*1.39.

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29) Two trains travel in the same direction at 50 and 32 km/hr. A man in the slower train observes that it takes 15 seconds for the faster train to completely pass him. What is the length of the slower train?

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30) In a Call Center the ratio of agents to manager is 50 : 1. If 500 more agents join, the ratio changes to 75 : 1. How many managers are there?

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31) If the rate of Compound interest and Simple interest is the same and the difference between the interest earned on a principal of $8000 over 2 years is$180, find the interest rate.

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32) ABC is a triangle with vertices A (4, 8), B (7, 3) and C (3, 1). Find the equation of the median AD.

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33) The average age of 40 boys of a class is 12 years. When 10 new boys are admitted, the average is increased by 0.1 year. What is the average age of the new boys?

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34) The LCM and HCF of the two numbers are 300 and 15 respectively. The difference between the two numbers is equal to the HCF. Find the numbers.

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35) Find the greatest three-digit number which when divided by 2, 3, 4 and 5 leaves a remainder of 1, 2, 3 and 4 respectively.

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36) A motorist travels to a place 100 kms away at an average speed of 50 km/hr and returns at 40 km/hr. The average speed of the journey is _________ km/hr?

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37) A can do a piece of work in 12 days. A and B together do the work in 8 days. How long would B alone take to complete the work?

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38) The maximum possible mark in an exam is 250. A got 210 and B got 10% less than C and 25% more than D. The marks of C are 90% of that of A. What is the percentage mark of B?

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39) Find the equation of a line with slope –4 and passing through the point (4, 5).

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40) The captain of a certain team of 11 players is 25 years old and the vice-captain is 3 years older. If the ages of these two players are excluded, the average age of the remaining players is 1 year less than the average age of the whole team. What is the average age of the whole team?

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41) The difference of squares of two numbers is 24 and one of the numbers is 5/7th of the other. Find the numbers.

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42) A number when divided by 2, 3, 5, 6, 7, 11, 13 and 14 leaves the reminders 1, 2, 4, 5, 6, 10, 12 and 13 respectively. What is the number?

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43) If I walk to my office at 6 km/hr, I arrive 6 minutes early. If however, I walk at 4 km/hr, I arrive 4 minutes late. What is the distance that I walk to reach the office?

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44) If 5/7 of an integer is 1125, 4/7 of the same integer will be…

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45) B earns 20% more than A, C earns 25% more than B and D earns 30 % more than C. If D earns $975, what does A earn? 46 / 200 46) The figure ABCD is a parallelogram. Find the perimeter of ABCD. AB = $2x+2y+7$ BC = $3x+2y-3$ DC = $4x-3y+10$ AD = $x+4y$ 47 / 200 47) The average age of 25 students of a class is 10 years. When a new student is admitted, the average age becomes 10.1 years. What is the age of the new student? 48 / 200 48) 20 years ago my age was 1/3rd of my present age. What is my present age now? 49 / 200 49) 20 years ago my age was 1/3rd of my present age. What is my present age now? 50 / 200 50) In a 200 meters race, A beats B by 20 meters, while in a 100 meters race B beats C by 5 meters. By how many meters will A beat C in a kilometer race assuming that speeds of A, B and C do not change in the races? 51 / 200 51) If 5a = 7b and 3b = 11c, find a : b : c 52 / 200 52) A house is sold by A to B at a profit of 10% and by B to C at a loss of 10%. If C pays$980,100 for it, what was the cost of the house for A?

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53) What is the length of the diagonal in the parallelopiped with dimensions 11, 8 and 6 units of length.

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54) The average attendance in a class for the first four days of the week is 32 and for the first 5 days is 33. How many students were present on the fifth day?

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55) The sum of $45 is made of 100 coins, partly of 50 cents and 25 cents. What is the number of 50 cents coins? 56 / 200 56) If $g(x)=\cfrac{3a-5}{2a+1}$, then what is the value of $\cfrac{5g(1)-3g(2)+10g(-1)}{8}$? 57 / 200 57) A and B cycle from Mumbai to Pune, a distance of 192 kms at 18 km/hr and 14 km/hr respectively. A reaches Pune and starts back for Mumbai. How far from Pune will he meet B? 58 / 200 58) Two numbers are in the ratio 5 : 6. When 4 is subtracted from each, the ratio becomes 4 : 5. The greater number is _____? 59 / 200 59) With the profit margin increased, a traders earns 25% more than before. If his earnings now are$800 per month, what was it before?

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60) A circular lawn of 98 meters is surrounded by a path of 14 meters wide. What is the area of the path in meters2?

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61) The average age of Allen and Beth is 40 years. If Chris were to replace Allen, the average would be 38 years and if he were to replace Beth, the average would be 42 years. What are the ages of Allen, Beth and Chris respectively?

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62) A temporary worker engaged on a contract basis is paid $10 every day he attends work and$5 is deducted from his salary as a fine every day he remains absent. If in a month of 30 working days, he earns $240, for how many days was he absent from work that month? 63 / 200 63) HCF of two numbers is 1/5th of a number and 1/7th of the other number. The difference between the numbers is 42. What is the LCM? 64 / 200 64) In a kilometer race B can give C a 100 meters and A 150 meters start. How many meters start can C give A? 65 / 200 65) In a game, A’s score was 2/7th of the total and B’s was 2/7th of the remainder. If A scored 32 runs more than B, what was the total score? 66 / 200 66) Of a certain sum, 1/3rd is invested at 3%, 1/6th at 6% and the rest at 8%. If the annual simple interest from this entire amount is$600, what is the original sum?

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67) The area of the four walls of a room is 1080 sq.ft. If the height and length of the room are in the ratio of 2 : 5 and the height and breadth are in the ratio 4 : 5. What is the area of the roof?

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68) The area of the four walls of a room is 1080 sq.ft. If the height and length of the room are in the ratio of 2 : 5 and the height and breadth are in the ratio 4 : 5. What is the area of the roof?

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69) What is the smallest number which 2880 must be divided by to make it a perfect square?

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70) What is the least number by which 2352 is to be multiplied to make it a perfect square?

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71) A train speeds past a pole in 20 seconds and speeds past a platform 150 meters long in 60 seconds. What is the length of the train?

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72) A can do a piece of work in 20 days and B in 40 days. A begins the work and there after A and B work on alternate days, the work then finishes during the course of the ________ day when ___________ is working.

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73) A money lender lends $400 for 2 years and$200 for 3 years, at the same rate on simple interest and receives $70 as interest. What is the interest rate? 74 / 200 74) A large cube is formed from the material obtained by melting three smaller cubes of side 3, 4 and 5 cms. What is the ratio of the total surface areas of the smaller cubes and the large cube? 75 / 200 75) The average temperature for the first 9 days was 20°C and that of the first 5 was 25°C and that for the last 5 days was 15°C. What was the temperature on the fifth day? 76 / 200 76) What is the value of a and b in $5\cfrac{1}{a}\times b\cfrac{3}{4}$ = 20? 77 / 200 77) $\cfrac{409}{4+\cfrac{3}{4+\cfrac{3}{4+\cfrac{3}{4}}}}$ = ? 78 / 200 78) A train traveling at 36 km/hr completely passes another train at 50% more speed but 50% of its length in the opposite direction in 12 secs. It takes 90 secs for the same train to pass a platform. Find the length of the platform. 79 / 200 79) A, B and C can together complete a piece of work in 10 days. If B does half of what A and C do in 1 day, in how many days can B alone finish the work? 80 / 200 80) Two typewriters were sold for$8000 each. The first was sold at a profit of 40% and the second at a loss of 40%. What was the cost of the first typewriter?

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81) Find the areas of the shaded region in the equilateral triangle.

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82) The average weight of 10 sacks of wheat is decreased by 1 lb when 2 of them 26 and 30 lbs are replaced by 2 rice sacks. What was the average weight of the two rice sacks?

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83) 10 years ago R was thrice as old as S was, but 10 years hence, he will be twice as old. What is R’s present age?

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84) In one of the following sets of fractions, the values increase progressively. Which is the one?

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85) A monkey climbs 30 meters of a pole during the day and slips down by 10 meters at night. Assuming that days and nights are equal, in how many days will the monkey scale a 120 meters high pole?

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86) What is A’s share of an amount of $7000, if he gets $\cfrac{1}{2}$ of what B and $\cfrac{1}{4}$ of what C gets? 87 / 200 87) The equal sides of an isosceles triangle are even integers only. What is the area of the triangle if the perimeter is 7 units? 88 / 200 88) Divide$1000 in two parts, so that if the two parts are invested @ 4% and 5% simple interest, the total yearly income may be $46.50. 89 / 200 89) The average age of 20 boys of a class is 12 years. Ten new boys are admitted and the average age increases by a year. The average age of the new boys is ________ years? 90 / 200 90) What is the number whose square is equal to the difference of the squares of 1884 and 1020? 91 / 200 91) What is the least number which must be subtracted from 10420 to make it a perfect square? 92 / 200 92) A monkey ascends a greased pole 21 meters high. In the first minute he ascends 5 meters and in the next minute descends 3 meters. If he continues this process, in how many minutes will he reach the top? 93 / 200 93) The ratio of the number of boys and girls in a school 432 students is 5 : 4. How many new girls should join the school so that the ratio becomes 1 : 1? 94 / 200 94) An article is sold at a profit of 20%. If both the cost price and selling price were to be$20 less, the profit made would be 10% more. What is the cost price of the article?

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95) A certain pole casts a shadow 24 feet long. At the same time another 3 feet high casts a shadow 4 feet long. How high is the first pole given that the heights and shadows are in proportion?

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96) The average age of a couple married four years ago was 25 years then. The average age of the family consisting of husband, wife and a child now is 20 years. What is the child’s present age?

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97) 8 mangoes and 6 apples can be purchased for $9.60 and 6 mangoes and 8 apples for$10. How much does each apple cost?

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98) $\cfrac{2^{5}\times 9^{2}}{8^{2}\times 3^{3}}=?$

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99) Mira rowed upstream in a stream flowing at the rate of 1.5 km/hr to a certain point and then rowed back stopping 2 kms short of the place where she originally started. If the rowing time was 2 hours 20 minutes and her uniform speed in still water was 4.5 km/hr, how far upstream did she go?

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100) A and B invest $3000 and$4000 respectively in a business. If A doubles his capital after 6 months, in what proportion should one divide that year’s profit?

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101) A man bought a watch marked at $400. He was given successive discounts of 15% and 10%. What did he pay for the watch? 102 / 200 102) A rectangular bin 4 feet long, 3 feet wide and 2 feet high is solidly packed with bricks of dimensions 8 inches, 4 inches and 2 inches. Find the maximum number of bricks that can go in the bin. 103 / 200 103) Nine men went to a restaurant. Eight of them spent$6 each for their meals and the ninth man spent $4 more than the average expenditure of all nine men. What is the average expenditure? 104 / 200 104) If $\cfrac{5}{3}+5+\cfrac{3}{5}+x=7$, what is x? 105 / 200 105) $\cfrac{6.5\times 4.7+6.5\times 5.3}{1.3\times 7.9-1.3\times 6.9}=?$ 106 / 200 106) After A has finished 1/2 of a piece of work in 10 days; B joins him after 5 days. Later A completes the work in 4 more days. In how many days would B alone complete the work? 107 / 200 107) 3% of rice stored in a godown is pilfered and 5% of the rest goes bad. If 11058 quintals of the rice remains in good condition, what was the original amount stored? 108 / 200 108) It takes 60 turns for one vessel to empty the tank. How many turns would it take totally to empty the tank if the vessel is used alternately with another one 1/3rd its capacity? 109 / 200 109) $\cfrac{\cfrac{1}{4}\times \left( \cfrac{1}{6}-\cfrac{1}{48} \right)}{\cfrac{1}{4}-\left( \cfrac{1}{6}-\cfrac{1}{48} \right)}\times \cfrac{\left( \cfrac{1}{4}-\cfrac{1}{6}-\cfrac{1}{48} \right)}{\left( \cfrac{1}{4}\times \cfrac{1}{6}-\cfrac{1}{48} \right)}=$? 110 / 200 110) B invests$500 more than A in business, but A’s investment in the business is for 4 months, whereas B’s investment is for 3 months only. If A’s share of total profit of $520 is$40 more than B’s. How much did A contribute to business?

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111) What is the compound interest on $4000 for 1 year @ 5% per annum payable half-yearly? 112 / 200 112) The sum of cubes of three numbers is 8072 and the ratio of the first to the second as also the second to the third is 3 : 2. What is the second number? 113 / 200 113) 50% of a number is equal to 7% of another number. The sum of these numbers is 171. What is the smaller of the two numbers? 114 / 200 114) Of an amount of$1500 divided between A, B and C, B’s share is $70 more than C’s and A’s share is$100 less than C’s. What is A’s share?

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115) The cost for transportation amounts to 5% of the cost price. What is the cost price of goods sold for $1890 at 20% profit on the total outlay? 116 / 200 116) Tom is 6 years elder to Dick. 20 years ago, Tom was 15 times older than Harry, but now Dick is twice as old as Harry. What is the age of Dick? 117 / 200 117) $\cfrac{4}{4+\cfrac{0.4-4.04}{4\times 0.91}}=?$ 118 / 200 118) The annual increase in population of a town is 5% If the present population is 70560, what was it two years ago? 119 / 200 119) Three years ago A’s age was double that of B’s. Seven years later, the sum of their united ages will be 83 years. How old is A? 120 / 200 120) $\cfrac{\sqrt{6}+\sqrt{7}}{\sqrt{5}-\sqrt{6}}=$? 121 / 200 121) A man, a woman or a boy can do a piece of work in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to finish the work in 1 day? 122 / 200 122) A bicycle is sold at a profit of 10%. Had it been sold for$10 less, the profit would have been 5% only. What is the cost of the bicycle?

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123) A student losses a mark for every wrong answer and scores 2 marks for every correct answer. If he answers all the 60 questions in an exam and scores 39 marks, how many of them were correct?

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124) Find the sum of reciprocal of two numbers whose sum is 12 and product is 32.

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125) The ratio of the number of ladies to gents at a party was 1 : 2, but when 2 ladies and 2 gents leave, the ratio became 1 : 3. How many people were at the party originally?

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126) $7500 is invested at 5% compound interest for 2 years. What is the interest in the 2nd year? 127 / 200 127) A man incurred a loss by selling a book for$60. Had he sold it for \$75, his gain would have been 4 times the former loss. Find the cost price of the book.

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128) Find the LCM of $\cfrac{4}{5}$, $\cfrac{3}{4}$ and $\cfrac{5}{7}$.

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129) The average age of 40 boys of a class is 12 years. When 10 new boys are admitted, the average is increased by 0.1 year. What is the average age of the new boys?

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130) In a examination of 5 subjects, all with the same maximum score, a candidate scored 60% in the aggregate and marks in proportion to 5 : 4 : 4 : 3 : 4 in individual subjects. What was his highest score in any subject?

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131) A is 2 years younger than B. If seven years back, A was 5/6th of B’s present age, what is half of B’s present age?

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132) Find the smallest from: $\cfrac{3}{7}$, $\cfrac{7}{20}$, $\cfrac{13}{25}$, $\cfrac{11}{20}$ and $\cfrac{15}{23}$.

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133) A certain number of men can finish a piece of work in 100 days. If however, there were 10 men less, it would take 10 days more to finish the work. How many men were there originally?