Question

Six years ago, the ratio of the ages of the two persons p and q was 3:2. Four years hence the ratio of their ages will be 8:7. What is p's age?

Answer 1

Answer:

$\huge\tt{Good Morning!!}$

$\huge\mathbb\orange{Solution..}$

At first,

6 years ago P's age was:-(p-6) years.

6 years ago q's age was:-(q-6) years.

First equation is:-

(p-6):(q-6)=3:2

or, (p-6)/(q-6)=3/2

or, 2(p-6)=3(q-6)

or, 2p-12=3q-18

or, 2p=3q-18+12

or, 2p=3q-6

So, p =(3q-6)/2..............(i)

Again, after 4 years,p's age will be:(p+4) years.

After 4 years,q's age will be:(q+4) years.

Second equation is:-

(p+4):(q+4)=8:7

or, (p+4)/(q+4)=8/7

or, 7(p+4)=8(q+4)

or, 7p+28=8q+32

or, 7p=8q+32-28

or, 7p=8q+4

So, p =(8q+4)/7.............(ii)

By substituting the value of (i) here we get,

(3q-6)/2=(8q+4)/7

or, 7(3q-6)=2(8q+4).

or, 21q-42=16q+8

or, 21q-16q=8+42

or,5q =50

or, q =50/5

So, q =10

So, q's age is:- 10 years.

Then by substituting the value of y in the (i) equation we get,

p =(3×10-6)/2

or, p =(30-6)/2

or, p=24/2

So, p =12

So, p's age is: 12 years.

Keep following ❤❤❤