Question

25. The ratio of the present ages of two brothers is
1:2 and 5 years back the ratio was 1 : 3. What
will be the ratio of their ages after 5 years?
(a) 1:4
(b) 2:3 (c) 3:5
(d) 5:6
Hig!
27.​

Answer 1

Given:

• Ratio of the present ages of two is 1:2.
• Before 5 years, ratio of their ages was 1:3.

To find:

• Ratio of their ages after 5 years?

Solution:

☯ Let Present ages of two brothers be x and 2x.

★ According to the Question:

• Before 5 years, ratio of their ages was 1:3.

Their ages before 5 years,

• Age of first brother = (x - 5) years
• Age of second brother = (2x - 5) years

Therefore,

➯ (x - 5)/(2x - 5) = 1/3

➯ 3(x - 5) = 2x - 5

➯ 3x - 15 = 2x - 5

➯ 3x - 2x = - 5 + 15

➯ x = 10

⠀⠀━━━━━━━━━━━━━━━━━━━━

Therefore,

• Present age of first brother, x = 10 years
• Present age of second brother, 2x = 2 × 10 = 20 years

And,

Their ages 5 years later,

• Present age of first brother = (10 + 5) = 15 years
• Present age of second brother = (20 + 5) = 25 years

Ratio of their ages 5 years later,

➯ 15/25 = 3/5

∴ Hence, Ratio of their ages 5 years later is 3:5.

Answer 2

Answer:

Given :-

• The ratio of the present ages of two brothers is 1:2 and 5 years back, the ratio was 1:3.

To Find :-

• What will be the ratio of their ages after 5 years.

Solution :-

Let, the present age of first brother be x

And, the present age of second brother be 2x

➣ Before 5 years,

First brother age = x - 5 years

And, second brother age will be 2x - 5

➣ Now, the ratio between their age will be,

⇒ $\dfrac{(x - 5)}{(2x - 5)}$ = $\dfrac{1}{3}$

According to the question,

⇒ $\dfrac{(x - 5)}{(2x - 5)}$ = $\dfrac{1}{3}$

By doing cross multiplication we get,

⇒ 3(x - 5) = 2x - 5

⇒ 3x - 15 = 2x - 5

⇒ 3x - 2x = - 5 + 15

➠ x = 10

Hence, the required ages will be,

✦ Present age of first brother = x = 10 years

✦ Present age of second brother = 2x = 2(10) = 20 years

Now, ratio of their ages after 5 years,

↦ $\dfrac{x + 5}{2x + 5}$

↦ $\dfrac{10 + 5}{20 + 5}$

↦ $\dfrac{15}{25}$

↦ $\dfrac{3}{5}$

➥ 3 : 5

$\therefore$ The ratio of their ages after 5 years is 3 : 5 .