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 (in
years)?
(a) 44 (b) 50 (c) 46
(d) 54 (e) 42​

Answer 1

Answer:

• The age of P is 46 year's.

Step-by-step explanation:

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 Equation (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.