CAT Questions

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Let Rajan's present age be 'x' years.
=> Then his daughter's present age is = x/3 years.
His mother's present age = 13x/9 years
Now, according to the question,
x + x/3 + 13x/9 = 125
=> x = 125x9/25 = 45
Therefore, required difference = 13x/9 - x/3 = 13x - 3x/9 = 10x/9
=> 10 x 45/9 = 50 years.

Let distance = x km and usual rate = y kmph.
Then, x/y - x/(y+3) = 40/60 --> 2y (y+3) = 9x ----- (i)
Also, x/(y-2) - x/y = 40/60 --> y(y-2) = 3x -------- (ii)
On dividing (i) by (ii), we get:

x = 40 km.

Hence, the missing number iss 25.

Food is processed by the stomach to provide energy for the functioning of the body.
Similarly, fuel is processed by the engine to provide energy for the functioning of automobile.

Let C.P.= Rs. 100.

Then, Profit = Rs.220, 

S.P. = Rs.320.

New C.P. = 125% of Rs. 100 = Rs. 125 

New S.P. = Rs.320.

Profit = Rs. (320 - 125) = Rs. 195

Required percentage = 195320×100== 60.9 =~ 61%

Given ratio of initial mixture of milk and water in Q = 5 : 3

Let the initial quantity of mixture in vessel Q = 8x

Let quantity of Milk = 5x and

Let quantity of water = 3x

According to the question,

5x + 10 x 353x + 10 x 25 = 85

=> 25x + 30 = 24x + 32

=> x = 2

Required Initial quantity of milk = 5x = 5 x 2 = 10 lit.

Arena is the special name for playground of Wrestling.

If heater D is used on the third day, heater B has to be used on the fourth day and A has to be used on the second day. But if A is used on second day, then either B or C has to be used on the first day. But if heater B is used on the first day, then according to the question, the requirement of having different heaters on the first day and fourth days would not be fulfilled. Hence the heater that would be used on the first day is C.