Question

4.
The ratio of the present ages of P and Q is 3 : 4. Five years ago, the ratio of their ages was 5:7.
Find their present ages.
a) 30 & 40 years b) 20 & 30 years c) 10 & 30 years d) 25 & 32 Years​

Answer 1

$\bullet\frak{ QuEsTion}$

The ratio of the present ages of P and Q is 3:4 . Five years ago , the ratio of their ages was 5:7.

Find their present ages.

a) 30 and 40 years

b) 20 and 30 years

c) 10 and 30 years

d) 25 and 32 years.

$\bullet \frak{SoluTion}$

Let, present ages of P and Q be 3 x and 4 x respectively .

then,

five years ago age of P should be = 3 x - 5

and

five years ago age of Q should be = 4 x - 5

it is given that ratio of their ages 5 years ago was 5 : 7

it means

$\tt \frac{3x-5}{4x-5} =\frac{5}{7} \\\\\tt corss\:multiplying\\\\\tt 21 x-35=20x-25\\\\\tt 21x-20x=35-25\\\\ \boxed{\tt x=10}$

Hence, the present ages of P and Q are

3 x = 30 years

and

4 x = 40 years

respectively.

so, the correct option is

a) 30 and 40 years.

Answer 2

a) 30 and 40 years

Explanation:

Given:

1. The ratio of the present ages of P and Q is 3: 4

2. Five years ago, the ratio of their ages was 5:7

To find:

Their present ages

Solution:

==> Ratio of P and Q is 3:4

==> Let, P=3x

==> Q = 4x

==> Five years ago,

==> P's age = 3x-5

==> Q's age = 4x-5

==> The ratio os their ages was 5:7

==> (3x-5):(4x-5)= 5:7

==> Write the ratio form as fraction

==> $\frac{3x-5}{4x-5}=\frac{5}{7}$

==> Doing cross multiplication

==> 7(3x-5)=5(4x-5)

==> 21x-35 = 20x-25

==> Separating coefficient of x and constant

==> 21x-20x =35-25

==> x = 10

==> The present age of P and Q

==> P = 3x

==> P =3(10)

==> P =30 years

==> Q = 4x

==> Q = 4(10)

==> Q = 40 Years

The present age of P is 30 years and Q is 40 years.

a) 30 and 40 years