# APTITUDE TEST 5

## About "Aptitude Test 5"

Aptitude Test 5 :

The test given in this section can be taken without any login credentials. At the end of the test, you can check you score as well as detailed answer for each question.

## Aptitude Test 5

Example Quiz 1

1. Find the least number which when divided by 35, leaves a remainder 25, when divided by 45, leaves a remainder 35 and when divided by 55, leaves a remainder 45.

 (A) 3405                   (B) 3435 (C) 3455                   (D) 3495

2. Two trains of equal length are running on parallel lines in the same direction at 46 kmph and 36 kmph. The faster train crosses the slower train in 36 seconds. The length of each train is

 (A) 48 m                 (B) 50 m (C) 52 m                 (D) 54 m

3. Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in:

 (A) 5.5 hrs             (B) 6.5 hrs (C) 7.5 hrs             (D) 8.5 hrs

4. A is faster than B . A and B each walk 24 km. The sum of their speeds is 7 km / hr and the sum of their time taken is 14 hrs. Then A's speed and B's speed (in kmph) are

 (A) 5 and 4                (B) 4 and 5 (C) 4 and 3                (D) 4 and 3

5. The total age of P and Q is 12 years more than the total age of Q and R. R is how many year younger to P?

 (A) 11 yrs                (B) 12 yrs (C) 13 yrs                (D) 14 yrs

6. A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.

 (A) 39                     (B) 40 (C) 41                     (D) 42

7. The speed of a boat in still water is 10 kmph. If it can travel 26 km downstream and 14 km upstream in the same time, the speed of the current is

 (A) 6 kmph                (B) 5 kmph (C) 4 kmph                (D) 3 kmph

8. The ratio of the prices of two houses was 16:23. Two years later when the price of the first has increased by 10% and that of the second by \$477, the ratio of the prices becomes 11:20. Find the original price of the first house.

 (A) \$ 648                (B) \$ 748 (C) \$ 848                (D) \$ 948

9. A merchant has 1000 kg of sugar, the part of which he sells at 8% profit and the rest at 18% profit. He gets 14% profit on the whole.The quantity sold at 18% profit is

 (A) 400 kg                 (B) 500 kg (C) 600 kg                 (D) 700 kg

10. The price of a table is \$ 400 more than that of a chair. If 4 tables and 6 chairs together cost \$3600, by what percentage is the price of the chair less than that of the table ?

 (A) 49%                    (B) 50% (C) 51%                    (D) 52%

## Detailed Explanation of Answers

 Question No.1 Question No.2 Question No.3 Question No.4 Question No.5 Question No.6 Question No.7 Question No.8 Question No.9 Question No.10 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} For each divisor and corresponding remainder, we have to find the difference. 35-25=10 45-35=10 55-45=10 we get the difference 10 (for all divisors and corresponding remainders) Now we have to find the L.C.M of (35,45,55) and subtract the difference from the L.C.M. L.C.M of (35,45,55) = 3465 Hence the required least number = 3465-10 = 3455 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Let "x" be the length of each train Total distance covered to cross each other = Sum of the lengths of the two trains Total distance covered to cross each other = x+x =2x m Relative speeds of the two trains = 46-36 = 10 kmph = 10X5/18 = 25/9 m/sec Distance = Speed X Time 2x = (25/9)X36 m 2x = 100 m x = 50 m Hence, the length of each train is 50 m jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Total work = 60 units. (L.C.M of 10,15,20) work done by the pipe A = 60/10 = 6 units/hr work done by the pipe B = 60/15 = 4 units/hr work done by the pipe C = 60/20 = 3 units/hr (Given:A is open all the time,B and C are open for one hour each alternately) 1st hour: (A+B) = 10 units/hr 2nd hour: (A+C) = 9 units/hr 3rd hour: (A+B) = 10 units/hr 4th hour: (A+C) = 9 units/hr 5th hour: (A+B) = 10 units/hr 6th hour: (A+C) = 9 units/hr When we add the above units, we get the total 57 units. Apart from the 6 hours of operation, to get the total work 60 units, A has to work for half an hour Because in one of hour work of A, we will get 6 units) Hence, time taken to fill the tank = 6.5 hours. jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Let "x" be the speed of A . Then speed of B = 7-x Time taken by A = 24/x Time taken by B = 24/(7-x) Time(A)+Time(B) = 14 hours. 24/x + 24/(7-x) = 14 24(7-x)+24x = 14x(7-x) 14x2-98x+168=0--->x2-7x+12=0 (x-4)(x-3)=0--->x = 4 and x = 3 Hence, the speed of A and B are 4 kmph and 3 kmph respectively. jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} From the given information, we have P+Q = 12+Q+R When we rearrange the above equation, we get P-R = 12+Q-Q P-R = 12 From the above equation, it is very clear that R is 12 years younger to P jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Let "x" be the average after 17th inning (Total run scored in 17 innings)/17 = x Total run scored in 17 innings = 17x ----(1) Average after 16th inning = x-3 (Total run scored in 16 innings)/16 = x-3 Total runs scored in 16 innings = 16(x-3) Total runs scored in 17 innings = 16(x-3)+87 ----(2) From (1) and (2), we get 16(x-3)+87 = 17x Solving the above equation, we get x = 39 Hence the batsman's average after 17th inning is 39. jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Let "x" be the speed of the current Speed upstream = (10-x) kmph Speed downstream = (10+x) kmph From the given information, we have 26/(10+x) = 14/(10-x) 26(10-x) = 14(10+x) 260-26x = 140+14x 40x = 120 x = 120/40 = 3 kmhr Hence the speed of the current is 3 kmph jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} From the given information, original of the 1st house = 16x original of the 2nd house = 23x After increment in prices, price of the 1st house = 16x + 10%of16x=16x+1.6x = 17.6x price of the 2nd house = 23x+477 After increment in prices, the ratio of the prices becomes 11:20 Then we have, 17.6x:(23x+477) = 11:20 20(17.6x) = 11(23x+477) 352x = 253x + 5247 99x = 5247 x = 53 Hence original price of the first house = 16X53 = \$848 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} From the given information, we have Profit on the first part (c) = 8% Profit on the second part (d) = 18% Profit on the whole (mixture) (m) = 14% Rule to find the ratio for producing mixture = (d-m):(m-c) (d-m):(m-c) = (18-14):(14-8) = 4:6 = 2:3 Quantity of the 2nd kind = 1000X3/5 = 600 kg The quantity sold at 18% profit is 600 kg jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Let "x" be the price of a chair. Then the price of a table = x+400 4 tables + 6 chairs = 3600 4(x+400) + 6x = 3600 4x+1600+6x = 3600 10x = 2000 ===>x = 200 So, price of a chair = \$400 and price of a table = \$800 Price of a chair is \$400 less than that of the table Percentage = (400/800)X100% = 50% Hence, the price of a chair is 50% less than that of the table.

After having practiced answering the above questions, we hope that the students would have understood, how to solve quantitative problems  easily.

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