Question

the age of A and B are in the ratio 3 ratio 8 6 year hence their age will be in the ratio 4 ratio 9 their present​

Answer 1

Question

the age of A and B are in the ratio 3 ratio 8, 6 year after their age will be in the ratio 4 ratio 9 their present ?

Solution

Given:-

• Age of A and B are in the ratio 3:8
• 6 year after their age will be in the ratio 4:9

Find:-

• The age of A and B

Explanation:-

Let,

• Age of A = x year.
• Age of B = Y year.

A/c to question,

( Age of A and B are in the ratio 3:8 )

➠ x : y = 3:8

➠ x/y = 3/8

➠ 8x - 3y = 0 -----------(1)

Again,

( 6 year after their age will be in the ratio 4:9 )

➠ (x +6):(y+6) = 4:9

➠ (x+6)/(y+6) = 4/9

➠ 9.(x+6) = 4.(y+6)

➠ 9x - 4y = 24-54

➠ 9x - 4y = -30 ----------(2)

Multiply by 4 in equ(1) and 3 in equ(2)

• 32x - 12y = 0
• 27x - 12y = -90

____________Sub. it's

➠ 32x - 27x = 90

➠ 5x = 90

➠ x = 90/5

➠ x = 18

keep value of x in equ(1),

➠ 8*18 - 3y = 0

➠ 3y = 144

➠y = 144/3

➠ y = 48

Hence

• Age of A = 18 years
• Age of B = 48 years.

______________________

Verification

( Age of A and B are in the ratio 3:8 )

➠ x : y = 3:8

keep value of x and y

➠ 18:48 = 3:8

Divide by 6 ,

➠ 3:8 = 3:8

L.H.S. = R.H.S.

Again,

( 6 year after their age will be in the ratio 4:9 )

➠ (x+6):(y+6) = 4:9

keep value x and y

➠ (18+6):(48+6) = 4:9

➠ (24):(54) = 4:9

Divide by 6

➠ 4:9 = 4:9

L.H.S. = R.H.S.

That's proved.

Hence, we can say that Age of A and B are right.