# Aptitude test series Set 4

1)   12 men and 18 boys working 7.5 minutes an hour complete a particular piece of work in 60 hours. If a boy’s work is half as efficient as a man’s work, how many boys will be needed to help 21 men to achieve twice the work in 50 hours working 9 minutes in an hour.

a. 42
b. 46
c. 48
d. 38
 Answer  Explanation ANSWER: 42 Explanation: 1 man is equivalent to 2 boys in work capacity. 12 men + 18 boys = 12 x 2 + 18 = 42 boys.Let the required number of boys be x. So Total number of people doing work = 21 men x 2 (according to work capacity) + x boys.Taking respective ratios as required:Given:=> Hours 50:60=> Minutes per hour 9: 15/2=> Work 1:2=> People: 42: 42 + x=> 50 x 9 x 1 x (42+x) = 60 x 15/2 x 2 x 42 => 42 +x = 84x = 42

2)   Speed of a man with current measures 15 km/hr. Speed of current is 2.5 km/hr. What is the speed of man against the current?

a. 12.5 kmph
b. 10 kmph
c. 9 kmph
d. 8.5 kmph
 Answer  Explanation ANSWER: 10 kmph Explanation: Let the speed of man in still water be x km/hrNow, speed with current=15 km/hrSpeed of current: 2.5 km/hrSpeed of man with current: Speed of man in still water+Speed of current=>15=x+2.5=>x=12.5Speed of man against the current: Speed of man in still water-Speed of current=>12.5-2.5=>10 km/hr

3)   Shweta buys a product at 25% discount rate. At what % over the cost price should she sell the product to make an overall 25% profit over the listed price?

a. 25
b. 33.333
c. 66.667
d. 40
 Answer  Explanation ANSWER: 66.667 Explanation: Let listed price of the product be x Hence at 25% discount rate the Cost Price will become: 3x/4Now to make an overall profit of 25% over listed price:SP = CP+(25/100)CP=> SP = x+x/4=>SP = 5x/4=>Selling Price over Cost price: (5x/4)-(3x/4)=>x/2=>%Selling price over Cost price: (x/2)/(3x/4)*100=>66.67%

4)   Presently a mixture in a tub contains substances A and B in the ratio of 7:5. If 9 litres of this solution is drawn out and B is added to the mixture in certain quantity the resulting mixture becomes 7:9. How much litres of liquid A was kept in the tub initially?

a. 32
b. 20
c. 27
d. 21
 Answer  Explanation ANSWER: 21 Explanation: Currently the mixture is in ratio of A/B: 7:5=> This means fraction of A in the solution: 7/12=> Fraction of B in the solvent: 5/12=>New concentration of A= 7-(7/12)9=>New concentration of B= 5-(5/12)9+x=> (7-(7/12)9)/(5-(5/12)9+x) = 7/9=>x=21

5)   Find the least number of 5 digits, which is exactly divisible by 89.

a. 24
b. 26
c. 27
d. 28
 Answer  Explanation ANSWER: 27 Explanation: No explanation is available for this question!

6)   A sum of money was to be divided amongst A and B in the ratio of 2:3. If the money is divided in the ratio of 3: 2, A will benefit by Rs. 75. The total money is

a. Rs. 325
b. Rs. 225
c. Rs. 250
d. Rs. 375
 Answer  Explanation ANSWER: Rs. 375 Explanation: No explanation is available for this question!

7)   A train runs across a post in 15 seconds and across a platform of length 100m in 25 seconds. Determine the length of this train:

a. A. 50 m
b. C. 200m
c. D. 130m
d. B. 150 m
 Answer  Explanation ANSWER: B. 150 m Explanation: Let us assume for this question that the length of train is x metres and it is assumed to be running at the speed of y m/sec.A pole is assumed as a point object.=>Time taken by the train to pass the pole= x/y=>15=x/y=>y=x/15Now, the train passes the platform which is 100 m in length in 25 seconds.=>x+100/y=25=>x+100/25=yEquating speed generated from both cases:x+100/25=x/15Therefore x = 150 metres.

8)   Find the missing number in the series.

2 , 3 , 6 , 0 , 10, -3 , 14...

a. 6
b. 2
c. -2
d. -6
 Answer  Explanation ANSWER: -6 Explanation: There are two series in the question1. Add 4 : 2+3 = 6, 6+4 = 102. Subtract 3 : 3-3 = 0, 0-3 - -3Thus, following the series:-3-3 = -6

9)   1 quarter Kg of potatoes cost 60 paise. Calculate the cost of 200 grams.

a. 48 paise
b. 62 paise
c. 54 paise
d. 26 paise
 Answer  Explanation ANSWER: 48 paise Explanation: Let 200 gm potato cost X paiseAccording to question, Cost of 1/4 Kg potato = 60 Paise=> Cost of 250 gm potato = 60 Paise => 1 Kg = 1000 gm => 1/4 Kg = 1000/4 gm = 250 gmBy direct proportion, more quantity, more cost200 grams : 250 grams = X : 60=> 200*60 = 250 X=> 12000 = 250 X=> X = 48=> Thus, the cost of 200 grams is 48 paise.

10)   A pineapple costs Rs 7 each and a watermelon costs Rs. 5 each. If I spend Rs 38 on total what is the number of pineapple I purchased?

a. 2
b. 3
c. 4
 Answer  Explanation ANSWER: Data Inadequete Explanation: The equation for this problem can be made as:5x + 7y =38Where x is the number of watermelons and y is the number of pineapples.Now test for 2, 3 and 4:For y = 2 5x + 14 =38x is not an integerFor y = 3 5x = 17X not an integerFor y =4 X = 2So 4 pineapples and 2 watermelons can be bought by 38 Rs.

11)   When 8% of a number is added to the number itself the result is 810. What is the number?

a. 700
b. 750
c. 722
d. 745.2
 Answer  Explanation ANSWER: 750 Explanation: No explanation is available for this question!

12)   A and B working separately can complete a piece of work in 9 and 12 days respectively. If they work alternatively starting from A in how many days will the work be completed?

a. 10.25 days
b. 11.5 days
c. 12.75 days
d. 9 days
 Answer  Explanation ANSWER: 10.25 days Explanation: A takes 9 days to complete a piece of work. B takes 12 days to complete a piece of work.=> In one day A came complete 1/9th of the task(x/9)=> In one day B can complete 1/12th of the job.(x/12)First day x/9th work will be done next day x/12th and so on:Together A and B can do x/9 + x/12 work.=>(x/9) + (x/12) = 7/36th work doneIn 10 days 35/36th of the work will be done.On 11th day it will be A’s chance. It takes A 1 day to complete 1/9th work.So, 1/36th work will be done in 1/4 days.=>10.25 days

13)   In how many ways can the letters of the word ENCYCLOPAEDIA be arranged such that vowels only occupy the even positions?

a. 453600
b. 128000
c. 478200
d. 635630
 Answer  Explanation ANSWER: 453600 Explanation: This is a simple problem of permutation and combination.Let us consider the number of times each alphabet is being used:E: 2N: 1C: 2Y: 1L: 1O: 1P: 1A: 2I: 1D: 1Now, total number of consonants: 7=> Total number of vowels: 613 letter word ENCYCLOPAEDIA has 6 vowels and there are 6 even spaces=>6 vowels can be arranged in 6 spaces in 6C6*6!/(2!*2!) ways.=>Rest of the letters (consonants) can be arranged in 7 spaces in 7C7*(7!/2!) waysHence total number of cases: 6!*7!/(2!*2!*2!)=>Answer: 453600

14)   When height of a tree is equal to the length of its shadow, what is the angle of elevation of the sun?

a. 30 deg
b. 60 deg
c. 90 deg
d. 45 deg
 Answer  Explanation ANSWER: 45 deg Explanation: No explanation is available for this question!

15)   How should we mix two rice packets to get one 1kg packet priced at Rs 8 when the prices of 1 kg packets of the two types are Rs 7.1 and Rs 9.2.

a. 4:3
b. 3:4
c. 4:5
d. 5:4
 Answer  Explanation ANSWER: 4:3 Explanation: No explanation is available for this question!

16)   Determine the number which should be subtracted from (14, 17) and (34, 42) to make remainders in same ratio?

a. 1
b. 2
c. 4
d. 7
 Answer  Explanation ANSWER: 2 Explanation: It is asked in the question that we need to find the number which when subtracted by 14,17 and 34,42 respectively will give their remainders in same ratio.Mathematically this can be represented in this form: => (14-x)/(17-x) = (34-x)/(42-x)=> Applying Componando &Dividendo=> C/D = (C+D)/(C-D)=> (31-2x)/(-3) = (76-2x)/(-8)=> 248-16x = 228-6x =>20=10x=>2=x

17)   Ratio of areas of incircle and circumcircle of an equilateral triangle is?

a. 1:4
b. 1:2
c. 2:1
d. 2:3
 Answer  Explanation ANSWER: 1:4 Explanation: No explanation is available for this question!

18)   What is the minimum number of years upon which SI on Rs 2600 at 6.67% interest rate will be in whole number?

a. 2
b. 6
c. 3
d. 4
 Answer  Explanation ANSWER: 3 Explanation: Simple Interest =Principal * Rate * TimePrincipal = 2600 RsInterest Rate = 6.67% => SI = 2600 * (20/3)*TimeSI of the number will be a whole number for the first time when time is three as denominator of rate is 3.Hence time should be set to 3 years.

19)   In a race, A beats B by 15 metres and C by 29 metres. If B and C run over the course together, B wins by 15 metres. What is the length of the course?

a. 225m
b. 120m
c. 220m
d. 160m
 Answer  Explanation ANSWER: 225m Explanation: Let X be the length of the courseaccording to the question, A beats B by 15 metres and C by 29 metresApplying this, If A runs X metres, B runs (X-15) and C runs ( X-29) metres.B and C together run, B runs X metres and C runs (X-15)=> If B runs 1 metre, C runs X-15/X=> B runs X-15 m, C runs (X-15/x) * (X-15)APPLYING THIS, X-29 = (X-15)(X-15) / XSolving,X2 -29X= X2 – 30 X + 225X = 225Thus, length of the course is 225 metres.

20)   LCM of two numbers is 495. HCF of these numbers is 5. If the sum of the numbers is 100, find out the difference between the two numbers.

a. 15
b. 12
c. 10
d. 20
 Answer  Explanation ANSWER: 10 Explanation: It is given that sum of two numbers is 100. Let the two numbers be x and 100 – x and HCF is 5 and LCM is 495=> We need to apply the formula: HCF x LCM = Product of two numbersWhich gives x(100 – x) = 495 x 5Solving the equation we get a quadratic which looks like this:x2 – 100x + 2475 = 0 => (x – 55)(x- 45) = 0Therefore, Two numbers are 55 and 45