Question

There are four friend, Megha, Ujjwala, Shivangi and Harsha. The age of Harsha is (P – 7) years. The ratio of the age of Harsha 7 years hence to the age of Ujjwala 2 years before is 6 : 5. The ratio of the age of megha 1 year before to the age of Harsha 3 years hence is 3 : 4. Harsha is 5 years older than Ujjwala, then find the age of shivangi whose age is 1 year less than average age of other 3 friends.
1. 77 years
2. 69 years
3. 61 years
4. 72 years

Answer 1

Correct Answer - Option 2 : 69 years

Given:

The age of Harsha is (P – 7) years.

The ratio of the age of Harsha 7 years hence to the age of Ujjwala 2 years before is 6 : 5.

The ratio of the age of megha to the age of Harsha 3 years hence is 3 : 4.

Formula used:

Average = sum of observation/number of observation

Calculation:

The age of Harsha is (P – 7) years

As, Harsha is 5 years older than ujjwala

Ujjwala's age = P – 7 – 5

⇒ (P – 12) years

According to the question,

⇒ ((P – 7) + 7)/(P – 12 – 2) = 6/5

⇒ P/(P – 14) = 6/5

⇒ 5P = 6P – 84

⇒ P = 84

Harsha age = 84 – 7

⇒ 77 years

Ujjwala age = 84 – 12

⇒ 72 years

Let the age of megha be M years,

Given that,

⇒ (M – 1)/(77 + 3) = 3/4

⇒ 4(M – 1) = 3 × 80

⇒ M – 1 = 60

⇒ M = 61 years

Megha's age = 61 years

Average of Megha, Harsha and ujjwala age

⇒ (61 + 77 + 72)/3

⇒ 70 years

The age of Shivangi is 1 years less than average of other 3 friends

⇒ 70 – 1

⇒ 69 years

∴ The age of shivangi is 69 years.