Question

if the present ages of a&b are in the ratio of 9:4 and after 7 years there ages are in the ratio of5:3 then find there present age​

Answer 1

Given :-

The present ages of a&b are in the ratio of 9:4.

After 7 years there ages are in the ratio of 5:3.

To find :-

Their present age.

Solution :-

✪The present ages of a & b are in the ratio of 9:4.✪

Let the present age of a be 9x years and the present age of b be 4x years.

★ After 7 years,

Age of a = (9x+7) years

Age of b = (4x +7) years

✪After 7 years there ages are in the ratio of 5:3✪

According to the question,

$\sf{(9x+7):(4x+7)=5:3}\\ \implies\frac{9x+7}{4x+7}=\frac{5}{3}\\ \implies\sf{27x+21=20x+35}\\ \implies\sf{27x-20x=35-21}\\ \implies\sf{7x=14}\\ \implies\sf{x=2}$

★Present age of a = 9×2 = 18 years

★Present age of b = 4×2 = 8 years

Therefore, present age of a is 18 years and present age of b is 8 years.

Answer 2

Given :-

• The present ages of a & b are in the ratio of 9:4.
• After 7 years there ages are in the ratio of 5:3.

To find :-

• Their present age.

Solution :-

✪The present ages of a & b are in the ratio of 9:4.✪

Let the present age of a be 9x years and the present age of b be 4x years.

★ After 7 years,

• Age of a = (9x+7) years

• Age of b = (4x +7) years

✪After 7 years there ages are in the ratio of 5:3✪

According to the question,

$\sf{(9x+7):(4x+7)=5:3}\\ \implies\frac{9x+7}{4x+7}=\frac{5}{3}\\ \implies\sf{27x+21=20x+35}\\ \implies\sf{27x-20x=35-21}\\ \implies\sf{7x=14}\\ \implies\sf{x=2}$

•Present age of a = 9×2 = 18 years

•Present age of b = 4×2 = 8 years

Therefore, present age of a is 18 years and present age of b is 8 years.

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Verification :-

• Present age of a = 18 years.

• Present age of b = 8 years.

Ratio of their present ages =9:4

→ 18 : 8 = 9 : 4

→ 9 : 4 = 9 : 4 (Verified )

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