Question

. The present ratio of ages of P & Q is 4 : 6. If

the sum of present ages of P & Q is 50 years,

then the sum of ages of P & Q before 4 years is​

Answer 1

$\textbf{\underline{\underline{Answer :-}}}$

The sum of their ages before 4 years is 42 years.

$\textbf{\underline{\underline{Explanation :-}}}$

$\textsf{\underline{\underline{Given :}}}$

Present age Ratio of P & Q = 4 : 6

Sum of the present ages = 50 years

$\textsf{\underline{\underline{To Find :}}}$

The sum of their ages before 4 years.

$\textsf{\underline{\underline{Solution :}}}$

Consider the age of P as 4x

Consider the age of Q as 6x

As given in the question : $\textsf{4x+6x=50}$

$\sf{\implies} \: 4x + 6x = 50$

$\sf{\implies} \: 10x = 50$

$\sf{\implies} \: x = \dfrac{50}{10}$

$\sf{\implies} \: x = 5$

$\boxed{\sf{\:x = 5 \: }}$

Value of 4x

$\sf{\implies} \: 4 \times 5$

$\sf{\implies} \: 20$

$\boxed{\textsf{P is 20 years old}}$

Value of 6x

$\sf{\implies} \: 6 \times 5$

$\sf{\implies} \: 30$

$\boxed{\textsf{Q is 30 years old}}$

Now, the sum of their ages before 4 years

⟹ P = 20 - 4

⟹ 16 years

⟹ Q = 30 - 4

⟹ 26 years

Sum =

$\sf{\implies} \: 16 + 26$

$\sf{\implies} \: 42$

$\therefore$ The sum of their ages before 4 years is 42 years.

Answer 2

Present Ratio of Ages of P and Q=4:6

Let P Present Age=4x

Let Q present Age=6x

Sum of Present Ages of P and Q=50 years

Means

P age+Q age=50 years

4x+6x=50

10x=50

x=50/10

x=5

Present Age of P=4x=4×5=20 years

Present Age of Q=6x=6×5=30 years

4 years Before

P age was=(20-4) years=16 years

Q age=(30-4) years=26 years

Sum of Their 4 years ago

16+26=42 years



Answer=42 years