Question

Q36. Sum of the age of P and Q is 64 years and the sum of age of P and R is 82 years. If age of Q is half of the age of R, then find the age of P (inyears)?
(a) 44 (b) 50 (c) 46
(d) 54 (e) 42​

Answer 1

Given

• Sum of the age of P and Q is 64 years.
• The sum of age of P and R is 82 years.
• Age of Q is half of the age of R.

To Find

• Age of P

Solution

_____________________

$\sf \: ~~~~~~~~\implies P + Q = 64 \: \: \: \: \: - - - - (1)$

$\sf \: ~~~~~~~~\implies P + R = 82 \: \: \: \: \: - - - - (2)$

$\sf \: ~~~~~~~~\implies Q = \dfrac{ R }{2 } \: \: \: \: \: - - - - (3)$

• Now In Equation (1)

$\sf~~~~~~~~\implies \: P + Q = 64$

$\sf \: ~~~~~~~~\implies P = 64 - Q$

• Putting the Value of P in Equ. (2)

$\sf ~~~~~~~~\implies \: 64 - Q + R = 82$

$\sf \: ~~~~~~~~\implies R = 82 - 64 + Q$

$\sf ~~~~~~~~\implies \: R = 18 + Q$

• Putting the Value of R Equation (3).

$\sf ~~~~~~~~\implies \: Q = \dfrac{ 18 + Q }{2 }$

$\sf ~~~~~~~~\implies \: 2 Q = 18 + Q$

$\sf \: ~~~~~~~~\implies 2 Q - Q = 18$

$\sf ~~~~~~~~\implies \: Q = 18$

• Putting the Value of Q in P= 64 -Q.

$\sf ~~~~~~~~\implies \: P= 64 -18$

$\sf \: ~~~~~~~~\implies P= 46$

• Hence the age of P is 46 year's.

Answer 2

Answer:

The age of P is 46 years.

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