Question

the present ages of A and B are in the ratio 7:5, Ten years later their ages will be in the ration 9:7. Find their present ages.

Answer 1

AnswerS

✳ Present age of A = 35years.

✳ Present age of B = 25years.

SOLUTION

Let us assume that the present age of A = 7x years $\longrightarrow$(1)

Let us assume that the present age of B = 5x years $\longrightarrow$ (2)

Then , after ten years

Age of A = 7x + 10 years.

Age of B = 5x + 10 years.

It is said in the question  that , ten years later their ages will be in the ration 9:7.

$\implies \sf \dfrac{7x + 10}{5x + 10} = \dfrac{9}{7}$

$\implies$ 7(7x + 10) = 9(5x + 10)

$\implies$ 49 x + 70 = 45x + 90

$\implies$ 49x - 45x = 90 - 70

$\implies$ 4x = 20

$\implies \sf x = \dfrac{20}{4}$

$\implies$ x = 5.

Now,Let us substitute x = 5 in (1) to find the present age of A.

$\implies$ Present age of A =  7x  = 7×5 = 35years.

Now,Let us substitute x = 5 in (2) to find the present age of B.

$\implies$ Present age of B = 5x = 5 × 5 = 25years.

Answer 2

Given :-

• The present ages of A and B are in the ratio 7:5.
• Ten years later their ages will be in the ration 9:7.

To Find :-

• Their Present Ages.

Solution :-

⟼ Let the Present age of A be 7x

⟼ Let the Present age of B be 5x

After 10 years :

⟼ After 10 years age of A will be 7x + 10

⟼ After 10 years age of B will be 5x + 10

According to the Question :

➞ (7x + 10) / (5x + 10) = 9/7

➞ 7 (7x + 10) = 9 (5x + 10)

➞ 49x + 70 = 45x + 90

➞ 49x - 45x = 90 - 70

➞ 4x = 90 - 70

➞ 4x = 20

➞ x = 20/4

➞ x = 5

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Therefore :

• Present age of A = 7x = 7 × 5 = 35years
• Present age of B = 5x = 5 × 5 = 25years

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