GATE Questions

---

According to the given data,

P + Q = 41 ......(1)

R - 1 = P + 2

R = P + 3

and

P + 4 = Q - 1

=> Q = P + 5 ....(2)

From (1)&(2)

P = 18

Q = 18 + 5 = 23

R = 18 + 3 = 21

=> P/S = 3/4

=> S = 4/3 x 18 = 24

Required Difference = S - R = 24 - 21 = 3.

Let the the age of the elder boy = E

Let the the age of the younger boy = Y

Given that Y = cube root of EY

=> Y3 = EY => E = Y2 .....(1)
By the condition of number replacement the age of the father is YE

The Mother's age = EY/2

But she is 3 years less than father => EY/2 + 3 = YE
2YE = EY + 6 ......(2)

Then now from the given options we can identify which satisfies the all the conditions.

Here Y =2 and E = 4 satisfies all the conditions.

3300 ----- 3% ↑ (1st time interval, 99) → 3399.

Here, time interval is given as half-yearly i.e. 6 months.

Let the amount of juice and water in original mixture '4x' litre and '3x' litre respectively.

According to given data,

4x/3x+6 =8/7

28x=24x+48

28x–24x=48

4x = 48

x = 12

Amount of juice = 4x = 4×12 = 48 litre.

Let the Oranges be 'O', Bananas be 'B' and Apples be 'A'

From the given data,

2O + 3B + 4A = 15 ...... (I)

3O + 2B + A = 10 ..... (II)

On adding (I) and (II),

5O + 5B + 5A = 25

O + B + A = 5

4O + 4B + 4A = 20.

Here the given series follows a pattern that,

2² - 0 = 4  

3² - 1 = 8  

4² - 2 = 14

5² - 3 = 22

6² - 4 = 32

Hence, the missing number is 32

Method 2 ::

The difference between 4 and 8 is 4, the difference between 8 and 14 is 6, the difference between 14 and 22 is 8. So the next difference between 22 and the next number will be 10 since it follows (4,6,8,10 - add +2 each time)

Hence, 22 + 10 = 32 is the missing number.

By trial and error method from the given options,

as 54 - 45 =  (1/11) x (45+54)  = 99/11  = 9

Hence this satisfies the given conditions.

Then the woman's husband age is 54.

Palm tree.