Six times the present age of P exceeds the present age of Q by 46 years. After 10 years, six times Q’s age will be 18 years less than five times P’s age at that time. What is the present age of Q (in years)?​

Correct option is B

Given:

Let the present ages of P and Q be P and Q years respectively.

Six times the present age of P exceeds the present age of Q by 46 years:

6P - Q = 46

After 10 years, six times Q’s age will be 18 years less than five times P’s age at that time:

6(Q+10) = 5(P+10) - 18

Find the present age of Q.

Solution:

From equation (2):

6Q + 60 = 5P + 50 - 18

6Q + 60 = 5P + 32

5P - 6Q = 28.........(Equation A)

From equation (1):

6P - Q = 46 .............(Equation B)

Multiply Equation B by 6:

36P - 6Q = 276

Subtract Equation A from this:

(36P - 6Q) - (5P - 6Q) = 276 - 28

31P = 248

P = 8

Substitute P = 8 in Equation (1):

6(8) - Q = 46

48 - Q = 46

Q = 2

Present age of Q = 2 years

Alternate Solution: