# APTITUDE TEST 4

Aptitude Test 1 :

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## Aptitude Test 4

Example Quiz 1

1. Find the square root of 123454321.

 (A) 111111                   (B) 11111 (C) 1111                       (D) 111

2. Find the time taken by a train 100m long running at a speed of 60 kmph to cross another train of length 80 m running at a speed of 48 kmph in the same direction.

 (A) 54 sec                 (B) 58 sec (C) 62 sec                 (D) 66 sec

3. A contractor decided to complete the work in 90 days and employed 50 men at the beginning and 20 men additionally after 20 days and got the work completed as per schedule. If he had not employed the additional men,how many extra days would he have needed to complete the work?

 (A) 26                    (B) 27 (C) 28                    (D) 29

4. A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, his speed(in kmph) must be

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

5. John's age after six years will be three-seventh of his father's age. Ten years ago the ratio of their ages was 1 : 5. What is John's father's age at present?

 (A) 47 yrs                (B) 48 yrs (C) 49 yrs                (D) 50 yrs

6. In Robert’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doesn't agree with Robert and he thinks that Robert's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Robert?

 (A) 62 kg                     (B) 65 kg (C) 67 kg                     (D) 69 kg

7. At his usual rowing rate Michael can travel 12 miles downstream in a certain river in six hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his 24 miles round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour?

 (A) 12⁄3 mph                 (B) 22⁄3 mph (C) 31⁄3 mph                (D) 51⁄3 mph

8. The monthly incomes of two persons are in the ratio 4:5 and their monthly expenditures are in the ratio 7:9. If each saves \$50 per month, find the monthly income of the second person.

 (A) \$ 500                     (B) \$ 450 (C) \$ 550                     (D) \$ 600

9. A milk vender has two cans of milk. The first contains 25% water and the rest milk. The second contains 50% water and the rest milk. How many liters of milk should he mix from each of the cans so as to get 12 liters of milk such that that the ratio of water to milk is 3:5?

 (A) (5,7)                      (B) (6,6) (C) (7,5)                      (D) (8,4)

10. The production of wheat was increased by 20% from the year 1994 to 1995. It was further increased by 25% from 1995 to 1996. The percentage change in the production of wheat from 1994 to 1996 was

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

 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 Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} In the given number, we have the first five natural numbers in ascending order up to 5. After 5, we have the first four natural numbers in descending order. Whenever we have a number like this and we want to find square root, we have to replace each digit by 1, up to the digit where we have the first n natural natural numbers in ascending order. So, in our number 123454321, we have to replace each digit by 1 up to 5. That is the square root of 123454321. Hence the square root of 123454321 is 11111. jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Total distance covered to cross each other = 100 + 80 = 180 m (when they run in opposite direction or same direction) Relative speed of the two trains = 60-18 = 12 kmph (running in the same direction) = 12X5/18 = 10/3 m/sec Time taken to cross each other = Distance/Speed = 180/(10/3) seconds =180X3/10 seconds =54 seconds Hence, time taken to cross each other = 54 seconds. jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Given Information: The work has to completed in 90 days (as per schedule) Total no. of men appointed initially = 50 50 men worked 20 days and completed a part of the work The remaining work is completed by 70 men (50+20=70) in 70 days (90-20=70) If the remaining work is completed by 50 men, no. of days taken by them = (70X70)/50 = 98 days. Hence, extra days needed = 98-70 = 28 days. jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} From the given information, Already 3 km distance (one half of the distance 6km) has been covered in 30 minutes or 1/2 hr. (two third of the total time 45 minutes) Remaining distance = 3 km Time available = 15 minutes or 1/4 hr Speed required = Distance / Time = 3/(1/4) kmph = 3X4 kmph = 12 kmph Hence, speed required to cover remaining distance is 12 kmph jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Ten years ago, age of John and his father are x and 5x Then, present age of John and his father are (x+10) and (5x+10) John's age after six years will be three-seventh of his father's age (x+10+6) = 3/7(5x+10+6) (x+16) = 3/7(5x+16) 7(x+16) = 3(5x+16) Solving the above equation, we get x=8 Present age of John's father = 5x+10 plug x = 8 Present age of John's father = 5(8)+10= 50 yrs jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Let "x" be John's weight According to Robert, we have 65 < x < 72 According to his brother, we have 60 < x < 70 According to his mother, we have x≤68 The values of "x" which satisfy all the above three conditions are 66, 67 and 68 Average of the above three values = (66+67+68)/3 = 201/3 = 67 kg Hence average of different probable weights of Robert is 67 kg jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Let "x" mph be speed in still water and "y" mph be speed of the current. Then, speed downstream = (x+y) mph 12/(x-y) - 12(x+y) = 6 By simplification, we get x2 = y2+4y ----(1) If the speed is doubled, speed in still water = 2x and speed of the current is same "y". Speed down stream = (2x+y) mph and speed up stream = (2x-y) mph 12/(2x-y) - 12(2x+y) = 1 By simplification, we get x2 = (24y+y2)/4 ----(2) Solving (1) and (2), we get y = 8/3 = 22⁄3 mph Hence speed of the current = 22⁄3 mph jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} From the given information, Income of the 1st person = 4x Income of the 2nd person = 5x Expenditure of the 1st person = 4x-50 Expenditure of the 2nd person = 5x-50 (Because each saves \$50 per month and Expenditure = Income - Savings) Expenditure ratio = 7:9 (4x-50):(5x-50) = 7:9 9(4x-50) = 7(5x-50) 36x-450 = 35x-350 x = 100 Hence income of the second person = 5X100 = \$500 jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Let the cost price of 1 liter pure milk be \$1 Milk in 1 liter mixture in the 1st can = 3/4 (that is 75%) Milk in 1 liter mixture in the 2nd can = 1/2 (that is 50%) Milk in 1 liter mixture in the final mix = 5/8 (from the given ratio w:m = 3:5) C.P of 1 liter mixture in the 1st can (c) = \$3/4 C.P of 1 liter mixture in the 2nd can (d) = \$1/2 C.P of 1 liter mixture in the final mix (m) = \$5/8 Rule to find the ratio for producing mixture = (d-m):(m-c) (d-m):(m-c) = 1/2-5/8:5/8-3/4 = 1/8:1/8 = 1:1 The above found ratio 1:1 says that equal quantity of milk should be taken from each of the cans. Since he wants to get 12 liters of milk, he should take 6 liters of milk from each of the cans. The correct answer is option (B) (6,6). jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Let 100 tons be the production of wheat in 1994 In 1994 ===> 100 tons In 1994-1995 ===> 120 tons (20% increment) In 1995-1996 ===> 150 tons (further 25% increment) When we look in to the above calculations, it is very clear that the production of wheat has been increased by 50 tons in 1996 from 100 tons in 1994 Percentage change = (50/100)X100 % = 50% Hence, the percentage change in the production of wheat from 1994 to 1996 was 50%

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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