Question

The sum of ages P and Q is 40 years. Five years ago, twice the age of P added to three times of age of Q was 70 years. Find their present ages.​

Answer 1

Given:-

Sum of ages of P and Q is 40 years

To find:-

Age of P and Q

Assumption:-

$\sf{Let \:the \:present \:age \:of \: P\:be\:x}$

$\sf{And\:present\:age\:of\:Q\:be\:y}$

Solution:-

ATQ,

$\sf{x+y = 40 \longrightarrow (I)}$

Five years ago,

$\sf{2(x-5)+3(y-5) = 70 \longrightarrow (ii)}$

From eq.(i)

$\sf{x+y = 40}$

= $\sf{x = 40-y}$

Substituting the value of x in eq.(ii)

= $\sf{2(x-5)+3(y-5)=70}$

$\sf{\implies 2(40-y-5)+3(y-5) = 70}$

$\sf{\implies 2(35-y) +3(y-5) = 70}$

$\sf{\implies 70-2y+3y-15 = 70}$

$\sf{\implies y+55 = 70}$

$\sf{\implies y = 70-55}$

$\sf{\implies y = 15}$

Putting the value of x in eq.(i)

= $\sf{x+y = 40}$

$\sf{\implies x+15=40}$

$\sf{\implies x = 40-15}$

$\sf{\implies x = 25}$

Therefore,

Age of P = x = 25 years

Age of Q = y = 15 years.

Verification:-

Sum of the ages of P and Q must be 40

$\sf{Age\:of(P+Q) = 40}$

= $\sf{25 + 15 = 40}$

= $\sf{40 = 40 \:\:\:[Hence\:Verified]}$