Question

At a birthday party Lemon juice and Orange juice were offered to the guests. If one-fifth of the guests drank lemon juice, one-fifth of the guests drank orange juice and 21 guests did not drink any of the juices, then find the total number of guests in the birthday party. 
1. 60
2. 45
3. 36
4. 55
5.

Answer 1

Correct Answer - Option 2 : 45

Given:

Number of guests who drank lemon juice = (1/5) of total number of guests

Number of guests who drank orange juice = (1/3) of total number of guests

Number of guests who did not drink any of the juices = 21 

Calculation:

Let the total number of guests in the birthday party be x.

According to the question,

Total number of guests = Number of guests who drank lemon juice + Number of guests who drank orange juice + Number of guests who drank nothing

⇒ x = (x/5) + (x/3) + 21

⇒ x = {(3x + 5x)/15} + 21

⇒ x = (8/15)x + 21

⇒ x - (8/15)x = 21

⇒ {1 - (8/15)}x = 21

⇒ {(15 - 8)/15}x = 21

⇒ (7/15)x = 21

⇒ x = (21 × 15)/7

⇒ x = 3 × 15

⇒ x = 45

∴ The total number of guests in the birthday party is 45.