Question

if the present ages of a and b are in the ratio 2:3.after 5 years their ages will be in the ratio 7:8.find their present ages(answer in detail)​

Answer 1

Given :

If the present ages 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

Solution :

Let the present age of A be 2x and B be 3x

• After 5 years
• A's age = 2x + 5
• B's age = 3x + 5

According to question

→ 2x + 5/3x + 5 = 7/8

• Cross multiplication

→ 8(2x + 5) = 7(3x + 5)

→ 16x + 40 = 21x + 35

→ 40 - 35 = 21x - 16x

→ 5 = 5x

→ x = 1

•°• Present age of A = 2x = 2years

•°• Present age of B = 3x = 3 years

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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,

Age of A be 2x + 5

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

According to the question,

↦ 2x + 5/3x + 5 = 7/8

By doing cross multiplication we get,

↦ 7(3x + 5) = 8(2x + 5)

↦ 21x + 35 = 16x + 40

↦ 21x - 16x = 40 - 35

↦ 5x = 5

↦ x = 5/5

➠ x = 1

Hence, the required present ages are,

✧ Present age of A = 2x = 2 × 1 = 2 years

✧ Present age of B = 3x = 3 × 1 = 3 years

∴ The present age of A is 2 years and the present age of B is 3 years.

Let's Verify :-

⇒ 2x + 5/3x + 5 = 7/8

By doing cross multiplication we get

⇒ 7(3x + 5) = 8(2x + 5)

⇒ 21x + 35 = 16x + 40

Put x = 1 we get,

⇒ 21(1) + 35 = 16(1) + 40

⇒ 21 + 35 = 16 + 40

⇒ 56 = 56

➦ LHS = RHS

Hence, Verified ✔