# Quantitative Aptitude Questions Daily Quiz Day – 32

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1) Two vessels contain mixtures of milk and water in the ratio of 8 : 1 and 1 : 5 respectively. The content of both of these are mixed in a specific ratio into a third vessel. How much mixture must be drawn from the second vessel to fill the third vessel (capacity 26 litres) completely in order that the resulting may be half milk and half water?

a) 12 litres

b) 14 litres

c) 10 litres

d) 13 litres

2) A and B can complete a work together in 8 days and the sum of the work done by them individually is 36 days. Which of the following can possibly represent the number of days taken by A and B individually to complete the work?

a) 18, 18

b) 16, 20

c) 12, 24

d) 15, 21

3) The ratio of the ages of father and son is 7:1. Calculate the average age of father and son 5 years from now if the respective ratio of their ages 4 years ago was 19:1.

a) 24 yrs

b) 25 yrs

c) 29 yrs

d) 28 yrs

4) Shatabdi Express has a capacity of 500 seats of which 10% is in the Executive class, rest being chair car. During one journey, the train was booked to 90% of its capacity. If Executive class was booked to 80% of its capacity, how many chair car seats were empty during that journey?

a) 450

b) 10

c) 40

d) 50

5) A discount of 20% is offered on a dress whose marked price is Rs. 800 while a discount of 15% is offered on a pair of trousers whose marked price is Rs. 1200. If I buy three dresses worth Rs. 800 and two pairs of trousers, what will be the effective discount I will get?

a) 45%

b) 35%

c) 32%

d) 17.5%

6) An article is sold at 20% discount thereby making a profit of 20 %. Calculate the percentage profit when the article is sold at 15% discount.

a) 25%

b) 12.5%

c) 31.5%

d) 27.5%

7) A bank offers 10% interest annually, compounded half yearly. A customer deposits Rs. 3600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is.

a) Rs 549

b) Rs 2232

c) Rs 558

d) Rs 279

8) The distance between Ambala and Chandigarh is approximately 50 kms. A car starts from Ambala at a speed which is 10 km/h more than its usual speed. The same car returned from Chandigarh at a speed which is 10 kmph less than its usual speed. The total journey time is 12 hours. Calculate how much time did it travel at slower speed?

a) 10 hrs

b) 2 hrs

c) 8 hrs

d) 6 hrs

9) The number of chocolates with P is 7/4 times of those with Q. The number of chocolates with R is 5/3 times of those with Q. What is the ratio of the number of chocolates with P to those with R?

a) 4:3

b) 20:21

c) 21:20

d) 3:4

10) In a family of husband, wife and a daughter, the sum of the husband’s age, twice the wife’s age, and thrice the daughter’s age is 85; while the sum of twice the husband’s age, four times the wife’s age, and six times the daughter’s age is 170. It is also given that the sum of five times the husband’s age, ten times the wife’s age and fifteen times the daughter’s age equals 450. The number of possible solutions, in terms of the ages of the husband, wife and the daughter, to this problem is

a) 3

b) 2

c) 0

d) Infinite solutions

Given, two vessels contain mixtures of milk and water in the ratio of 8 : 1 and 1 : 5 respectively.

Amount of water in 1st vessel = 1/9

Amount of water in 2nd vessel = 5/6

Final mixture has half milk and half water

Amount of water in 3rd vessel =1/2

Let the volume taken from 1st vessel be x, then the volume of mixture is taken from 2nd vessel = 26 – x ⇒ x = 12 litres

Volume drawn from 2nd vessel = 26 – 12 = 14 litres

Let the number of days taken by A and B to complete the work individually be ‘A’ days and ‘B’ days respectively.

Then, A’s work in one day and B’s work in one day can be written as 1/A and 1/B and if they work together, one day’s work can be obtained as (1/A + 1/B = (A + B) / AB).

Number of days taken to complete the work together = (AB / (A + B))

8 = (AB / 36)

AB = 288

Among the given options, only (12, 24) satisfies both the conditions {(12 + 24 = 36) and (12 * 24 = 288)}.

Let the present ages of father and son be 7x and x

Now according to the question

=> (7x-4)/(x-4) = 19/1

=> 7x-4 = 19x-76

=> 12x = 72

=> x = 6

Father’s age = 7*6 = 42 years

=> Son’s age = 6 Years

Father age after 5 years = 42+5 = 47

=> Son’s age after 5 Years = 6+5 = 11

Average age = (47+11) /2

= 58/2

= 29 years

Total number of seats = 500

No of Executive class seats = 10% of 500 = 50 seats.

No of chair cars = 500 – 50 = 450 seats.

During journey, 90% seats booked = 450 seats booked in total.

Now, executive class was booked 80% of its capacity = (80/100) × 50 = 40 seats booked.

Now, there were 50 not booked seats in total = 50 – 10 = 40 not booked chair cars.

∴ 40 chair cars were empty during the journey.

Total discount on buying three dresses = 3 * (20% * 800) = Rs. 480

Total discount on buying two pairs of trousers = 2 * (15% * 1200) = Rs. 360

Total discount = Rs. 480 + Rs. 360 = Rs. 840

Total marked price = 3 * Rs. 800 + 2 * Rs. 1200 = Rs. 4800

Effective discount = 840/ 4800 * 100 = 17.5%

=> Let C.P be 100,

=> and marked price =m

=> S.P after 20 % profit and 20% discount

=> S.P= 100*(1+20/100)

=> =120

=> Also S.P = m*80/100

=> (80/100)m=120

=> m = 150

=> Now S.P after 15 % discount 150(1-15/100)

=> =127.5

=> Profit 127.5-100=27.5 and %age profit = 27.5%

We know that,

Amount received after compound interest = P(1 + r/100)n

Where, P is the principal amount

r is the rate of interest

n is the number of intervals

Amount received at the end of year is given by,

A = 3600(1 + 10/200) + 3600 (1 + 10/200)1

A = 3600 (1 + 0.05)2 + 3600 (1 + 0.05)1

A = 3969 + 3780 = 7749

Principal Amount = 3600 + 3600 = Rs. 7200

∴ Interest gained = 7749 – 7200 = Rs. 549

=> Total time taken = 12 hours

=> Time taken from Ambala to Chandigarh = 50/(x+110)

=> x = usual speed

=> and time taken from Chandigarh to Ambala = 50 / (x-10)

=> 50/(x-10) + 50 (x+10) = 12

=> Solving we get x = 15

=> slower speed = 15 – 10 = 5 km/h

=> Time taken = 50/5 = 10 hours

The number of chocolates with P is 7/4 times of those with Q.

P = (7/4) * Q or 4P = 7Q — (1)

The number of chocolates with R is 5/3 times of those with Q.

R = (5/3) * Q or 3R = 5Q — (2)

Multiplying (1) by 5 and (2) by 7, we get-

20P = 35Q = 21R or

P/R = 21/20

Let the age of husband wife and daughter be denoted by h, w and d respectively

⇒ h + 2w + 3d = 85 – – – – – – – – (i)

⇒ 2h + 4w + 6d = 170 – – – – – – – – (ii)

⇒ 5h + 10w + 15d = 450 – – – – – – – – (iii)

Multiplying the first equation by 5 we get

⇒ 5h + 10w + 15d = 425

But Eq (iii) gives 5h + 10w + 15d = 450

So, No solutions possible

∴ No solutions possible.