Question

The present ages of A and B are in the ratio 4:5. Ten years ago, their ages were in ratio 3:4. What are their present ages?

Answer 1

Given :

• The present ages of A and B are in the ratio 4:5.
• 10 years ago, their ages were in ratio 3:4.

To find :

• Their present ages.

Solution :

Consider,

• Present age of A = 4x years
• Present age of B = 5x years

10 years ago,

• Age of A = (4x-10) years
• Age of B = (5x-10) years

According to the question :-

• 10 years ago, their ages were in ratio 3:4.

$\sf\to{(4x-10):(5x-10)=3:4}$

$\sf\to{\dfrac{4x-10}{5x-10}=\dfrac{3}{4}}$

$\sf\to{16x-40=15x-30}$

$\sf\to{16x-15x=40-30}$

$\sf\to{x=10}$

★Present age of A = 4×10 = 40 years

★ Present age of B = 5×10 = 50 years.

Answer 2

$\mathcal{\huge{\fbox{\red{Question\:?}}}}$

✴ The present ages of A and B are in the ratio 4:5. Ten years ago, their ages were in ratio 3:4. What are their present ages?

$\mathcal{\huge{\fbox{\green{AnSweR:-}}}}$

✒ Present age of A is 40 years & B is 50 years.

$\mathcal{\huge{\fbox{\purple{Solution:-}}}}$

Given :-

• The present ages of A and B are in the ratio 4:5.

• Ten years ago, their ages were in ratio 3:4.

To find :-

• Their present ages of A & B.

Calculation :-

According to the question,

• The present ages of A and B are in the ratio 4:5.

The the ages in term of x. Hence,

▶Present age of A is 4x yrs.

▶Present age of B is 5x yrs.

• Ten years ago,

▶Age of A = (4x-10) years.

▶Age of B = (5x-10) years.

• The ages were in ratio 3:4.

➡ (4x−10):(5x−10)=3:4

➡ $\dfrac{4x - 10}{5x - 10} = \dfrac{3}{4}$

➡ 4× (4x−10) = 3 × (5x−10)

➡ 16x−40=15x−30

→16x−15x=40−30

→x=10

We considered above ,

• Present age of A is 4x yrs = 4 × 10 = 40 yrs.

• Present age of B is 5x yrs. = 5 × 10 = 50 yrs.

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