# LIC AAO Mains Quantitative Aptitude Questions 2019 (Day-07)

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Â 1) A tank contains a mixture of milk and water. Total quantity of a mixture of 170 litres and the ratio of milk to water in the mixture is 12: 5. If X litre of the mixture is taken out and only 40 litres of water is left out in the mixture, then find the value of X?

a) 38 litres

b) 42 litres

c) 46 litres

d) 34 litres

e) None of these

2) The sum of the present age of P, Q and R is X. Present age of R is X â€“ 50. After 12 years, the age of R is equal to the present age of Q. After 6 years, the age of P is equal to the present age of Q. Find the present age of R?

a) 18 years

b) 20 years

c) 16 years

d) 22 years

e) None of these

3) A man covered one-fourth of the distance by bus with a speed of 40 km/hr and the remaining distance will be covered by bike with a speed of 60 km/hr. Find the total distance covered by the man, if the total time taken by him is 5 hours 15 mins?

a) 220 km

b) 340 km

c) 280 km

d) 300 km

e) None of these

4) Agila, Manoj and Prithika enter into a partnership. Agila invests 2 times as much as Manojâ€™s investment and Manoj invests 4/7th of Prithikaâ€™s investment. If the total profit earned at the end of the year is Rs. 123500, then find the share of Manoj?

a) Rs. 28000

b) Rs. 22000

c) Rs. 26000

d) Rs. 30000

e) None of these

5) Two pipes can fill an empty tank in 3 hours 15 min. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the tank, it takes 45 min more to fill the tank. If the tank is full, at what time would the leakage empty the full tank?

a) 16 hours 25 min

b) 15 hours 45 min

c) 17 hours 20 min

d) 18 hours 30 min

e) None of these

Directions (Q. 6 â€“ 10): Study the following information carefully and answer the given questions

The following line graph shows the ratio of number of boys to that of number of girls passed from two different schools in the year 2012 to 2017.

6) If in the year 2014, the total number of boys in School A is 78 and the total number of girls in School B in the year 2013 is 80, then find the difference between the total number of girls in School A in the year 2014 to that of boys in School B in the year 2013?

a) 212

b) 306

c) 258

d) 344

e) None of these

7) The number of boys passed in School A in the year 2015 is approximately what percentage of the number of girls passed in School A in the same year?

a) 125 %

b) 140 %

c) 112 %

d) 105 %

e) None of these

8) If the number of girls passed from School A in the year 2016 and the number of girls passed from School B in the year 2017 is equal, then the number of boys passed from school A in the year 2016 is approximately what percentage more/less than the number of boys passed from School B in the year 2017?

a) 21 % less

b) 7 % more

c) 7 % less

d) 21 % more

e) 14 % more

9) If the number of boys passed from School A in the year 2012 is 108, which is equal to the number of boys passed from School B in the year 2013, then find the ratio of number of girls passed from School A in the year 2012 to that of total number of girls passed from School A in the year 2012 and School B in the year 2013?

a) 8: 5

b) 2: 1

c) 7: 4

d) 4: 1

e) None of these

10) In which year, the highest number of girls passed in School A?

a) 2013

b) 2015

c) 2016

d) Canâ€™t be determined

e) None of these

According to the question,

Total milk in the mixture = 170*(12/17) = 120 litres

Total water in the mixture = 170*(5/17) = 50 litres

After X litre of the mixture is taken out,

Only 40 liters of water is left out.

% of water taken out in the mixture = (10/50)*100 = 20 %

If 20 % of water is taken out means 20 % milk also taken out.

So, the milk left in the mixture = 120*(80/100) = 96 litres

Total mixture is taken out = X = 10 + 24 = 34 litres

The sum of the present age of P, Q and R = X

Present age of R = X â€“ 50

After 12 years, the age of R = The present age of Q

The present age of Q = X â€“ 50 + 12 = X â€“ 38

After 6 years, the age of P = The present age of Q

The present age of P = X â€“ 38 – 6 = X â€“ 44

According to the question,

X â€“ 44 + X â€“ 38 + X â€“ 50 = X

3x â€“ 132 = x

2x = 132

X = 66

The present age of R = X â€“ 50 = 66 â€“ 50 = 16 years

Total time taken by him = 5 hours 15 min = 5 15/60 = 5 (1/4) hours

T = D/S

(x/4)/40 + (3x/4)/60 = 5 1/4

x/40 + 3x/60 = (21/4)*4

(3x + 6x)/120 = 21

9x = 21*120

X = (21*120)/9

X = 280 km

The investment of Agila to Manoj = 2: 1

Manojâ€™s investment = (4/7)*Prithikaâ€™s investment

The investment of Manoj and Prithika = 4: 7

The investment of Agila, Manoj and Prithika = 8: 4: 7

Here, the period is not given. So,

The ratio of investment = The ratio of profit

Total profit = Rs. 123500

19â€™s = 123500

1â€™s = 6500

The share of Manoj = 4â€™s = Rs. 26000

Two pipes can fill an empty tank in = 3 hours 15 min = 3 15/60 = 3 1/4

But due to the leakage, it takes 45 min more,

So, Total time taken to fill the tank = 4 hours

Required number of hours = 4/13 â€“ (1/4) = (16 â€“ 13)/52 = 3/52

The leakage empty the full tank in 52/3 = 17 hours 20 min

Directions (6-10):

In the year 2014, the ratio of boys to girls in School A = 2.6 = 26/10 = 13/5

The total number of boys in School A is 78

= > 13â€™s = 78

= > 1â€™s = 6

Total girls in School A = 5â€™s = 30

In the year 2013, the ratio of boys to girls in School B = 3.6 = 36/10 = 18/5

The total number of girls in School B = 80

= > 5â€™s = 80

= > 1â€™s = 16

Total number of boys in School B = 18*16 = 288

Required difference = 288 â€“ 30 = 258

The ratio of boys to that of girls passed in School A in 2015 = 1.4

= > 14/10 = 7/5

Required % = (7/5)*100 = 140 %

Let the number of girls passed from School A in the year 2016 and the number of girls passed from School B in the year 2017 be x,

The ratio of boys to girls in School A in 2016,

= > (BA/GA) = 2.2

= > BA = 2.2x

The ratio of boys to girls in School B in 2017,

= > (BB/GB) = 2.8

= > BB = 2.8x

Required % = [(2.8x â€“ 2.2x)/2.8x]*100 = (0.6/2.8)*100 = 21.42 %

= 21 % less

The ratio of number of boys to that of girls in School A in 2012

= > 1.8 = 18/10 = 9/5

The number of boys passed from School A in the year 2012 = 108

= > 9â€™s = 108

= > 1â€™s = 12

The number of girls passed from School A in the year 2012 is,

= > 5â€™s = 5*12 = 60

The ratio of number of boys to that of girls in School B in 2013

= > 3.6 = 36/10 = 18/5

The number of boys passed from School B in the year 2013 = 108

= > 18â€™s = 108

= > 1â€™s = 6

The number of girls passed from School B in the year 2013 is,

= > 5â€™s = 30

Required ratio = 60: 30 = 2: 1