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

(1) 52 years (2) 50 years

(3) 42 years (4) 26 years

plz explain

Answer 1

Answer :-

◾Information provided :-

▪️Ratio of ages of P & Q = 4 : 6

▪️Sum of ages of P & Q = 50 years

◾Question to be answered :-

▪️The ages of P & Q 4 years ago

➡️Solution :-

▪️Let the common divisor of ratio be "x"

▪️Then -->

P + Q = 50

$\implies 4x + 6x = 50$

$\implies 10x = 50$

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

$\implies x = 5$

• Hence age of

P = 4x

= 4(5)

= 20 years

Q = 6x

= 6(5)

= 30 years

◾Now sum of ages 4 years ago

= (age of P - 4) + (age of Q - 4)

= (20 - 4) + (30 - 4)

= 16 + 26

= 42 years

Option (3)

Answer 2

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

Option (3) 42

The sum of the ages before 4 years is 42.

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

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

Present ratio of ages of P and Q = 4 : 6

Sum if their 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

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

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

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

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

Value of 4x

$\implies$ 4 × 5

$\implies$ 20

Present age of P = 20 years

Value of 6x

$\implies$ 6 × 5

$\implies$ 30

Present age of Q = 30 years

Ages Before 4 years :

$\implies$ P = 20 - 4 = 16

$\implies$ Q = 30 - 4 = 26

Sum of the ages =

$\implies$ 16 + 26

$\implies$42

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

$\therefore$ The answer is Option (3) 42.