Solution MAINS HARD LEVEL SET 1

1.Three partners invested capital in the ratio 2 : 7 : 9. The time period for which each of them invested was in the ratio of the reciprocals of the amount invested. Find the share of the partner who brought in the highest capital, if profit is Rs. 1080.

 1)

Rs. 120

 2)

Rs. 360

 3)

Rs. 540

 4)

Rs. 420

 5)

None of these

Solution Key:
Capital invested ratio = 2 : 7 : 9
time period invested ratio = ½ : 1/7 : 1/9
share ratio = 2 x ½ : 7 x 1/7 : 9 x 1/9 = 1 : 1 : 1
Required share = 1/3 x 1080 = Rs. 360


2.Two boys are playing in the ground. Both the boys are less than 10 years old. Age of the younger boy equal to the cube root of the product of the age of the two boys. If we place the digit representing the age of the younger boy to the left of the digit representing the age of the elder boy, we get the age of the father of the younger boy. Similarly, if we place the digit representing the age of the elder boy to the left of the digit representing the age of the younger boy and divide the figure by 2, we get the age of the mother of the younger boy. The mother of the younger boy is younger than his father by 3 years. Then, what is the age of the younger boy?

1)

3

 2)

4

 3)

2

 4)

5

 5)

None of these

Solution Key:
Here we can go by the options one by one keeping eye on the given conditions. 
Lets assume younger boy age is 3 years old, then elder one will be < 10 and product of their ages has to be a perfect cube.,br> So according to this Elder one age will be 9.
So the age of the father of the younger boy = 39 years old and age of mother will be 93/2 = 46.5 years old.
But difference of their ages must be 3 years, so this is not satisfying here. 
Similarly if we go bye the option 2, then Father age will be 24 while mother age will be 21 year and difference between them is 3 years.


3.A student purchased a computer system and a colour printer. If he sold the computer system at 10% loss and the colour printer at 20% gain, he would not lose anything, but if he sells the computer system at 5% gain and the colour printer at 15% loss, he would lose Rs. 800 in the bargain. How much did he pay for the colour printer?

1)

Rs. 9,000

 2)

Rs. 16, 000

 3)

Rs. 8,000

 4)

Rs. 5, 334

 5)

None of these

Solution Key:
C.P. of comp. system = Rs. A
CP of colour printer = Rs. B
0.9A + 1.2 B = A + B
0.2 B = 0.1 A
A = 2B
(A+ B) – (1.05A + 0.85B) = 800
(2B + B) – (2.10B + 0.85 B) = 800
3B – 2.95 B = 800
0.05 B = 800
B = 800/5 x 100 = 16, 000

4. A group consisting of 25 teachers, 20 engineers, 18 doctors and 12 salesmen visited a fair and spent Rs. 1330 altogether. It was found that 5 teachers spent as much as 4 engineers; 12 engineers spent as much as 9 doctors and 6 doctors spent as much as 8 salesmen. If every person in a professional group spent the same amount. The amount spent by each engineer is

1)

Rs. 18

 2)

Rs. 17.50

 3)

Rs. 14

 4)

Rs. 21

 5)

None of these

Solution Key:
5T = 4E ….(i)
12 E = 9D …(ii)
6D = 8$ …(3)
9D = 12$ …(4)
from 1
25T = 20E
25T + 20E + 18D + 12$ = 1330
20E + 20E + 24E + 12E = 1330
76E = 1330
E = 17.50

5.A train consists of 12 bogies, each bogie is 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, two bogies were detached. The train now crosses a telegraph post in

 1)

15 sec

 2)

12 sec

 3)

18 sec

 4)

20 sec

 5)

None of these

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Solution Key:
Length = 12 x15 = 180
S x 18 = 180
= S = 10 m/s
2 bogies = 2 x 15 = 30 m
Time for 30 m = 30/10 = 3s
New Time = 18 – 3 = 15