Question

the present age of A and B are in the ratio 2:3.After five years their ages will be in the ratio 7:8.Find the present ages.​

Answer 1

Given:-

• The present age of A and B are in the ratio 2:3
• After 5 years their ages will be in the ratio 7:8

To Find:-

• Present ages of A and B

Assumption:-

• Let the ratio common be x for present ages.
• Age of A = 2x
• Age of B = 3x

Solution:-

It is given that after 5 years their ages will be in the ratio 7:8.

Hence,

After 5 years,

Age of A = 2x + 5

Age of B = 3x + 5

According to The question:-

(2x + 5) : (3x + 5) = 7 : 8

⇒ (2x + 5)/(3x + 5) = 7/8

⇒ 8(2x + 5) = 7(3x + 5)

⇒ 16x + 40 = 21x + 35

⇒ 16x - 21x = 35 - 40

⇒ - 5x = -5

⇒ x = -5/-5

⇒ x = 1

∴ We got the value of x as 1.

Putting the value of x in the ratio whose constant we assumed to be x:-

• Present age of A = 2x = 2 × 1 = 2 years
• Present age of B = 3x = 3 × 1 = 3 years.

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Verification!!!

Let us see whether after 5 years the ratio of their age becomes 7 : 8 or not.

After 5 years,

Age of A = 2 + 5 = 7 years

Age of B = 3 + 5 = 8 years

Ratio:-

= 7 : 8

∴ We got the ratio of both of their ages in the ratio 7:8.

Hence Verified!!!

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Answer 2

Answer:

Given :-

• The present age of A and B are in the ratio of 2 : 3. After 5 years their ages will be in the ratio of 7 : 8.

To Find :-

• What is their present ages.

Solution :-

Let, the present age of A be 2x

And, the present age of B will be 3x

After 5 years,

The age of A be 2x + 5

And, the age of B will be 3x + 5

According to the question,

⇒ $\sf \dfrac{2x + 5}{3x + 5} =\: \dfrac{7}{8}$

By doing cross multiplication we get,

⇒ $\sf 7(3x + 5) =\: 8(2x + 5)$

⇒ $\sf 21x + 35 =\: 16x + 40$

⇒ $\sf 21x - 16x =\: 40 - 35$

⇒ $\sf 5x =\: 5$

⇒ $\sf x =\: \dfrac{\cancel{5}}{\cancel{5}}$

➠ $\sf\bold{\red{x =\: 1}}$

Hence, the required ages are,

✧ Present age of A = 2x = 2(1) = 2 years

✧ Present age of B = 3x = 3(1) = 3 years

$\therefore$ The present age of A is 2 years and the present age of B is 3 years.

${\purple{\boxed{\large{\bold{VERIFICATION :-}}}}}$

↦ $\sf \dfrac{2x + 5}{3x + 5} =\: \dfrac{7}{8}$

By putting x = 1 we get,

↦ $\sf \dfrac{2(1) + 5}{3(1) + 5} =\: \dfrac{7}{8}$

↦ $\sf \dfrac{2 + 5}{3 + 5} =\: \dfrac{7}{8}$

↦ $\sf\bold{\green{\dfrac{7}{8} =\: \dfrac{7}{8}}}$

➦ LHS = RHS

Hence, Verified ✔