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A bag is full of white balls. These balls are divided into two parts in the ratio 2 ∶ 1. The balls in the first part are further divided in ratio 4 ∶ 1 and painted red and yellow respectively. The balls from the second part are divided in the ratio 1 ∶ 3 and painted red and green respectively. If 37 balls were painted red, how many total balls are there?

A bag is full of white balls. These balls are divided into two parts in the ratio 2 ∶ 1. The balls in the first part are further divided in ratio 4 ∶ 1 and painted red and yellow respectively. The balls from the second part are divided in the ratio 1 ∶ 3 and painted red and green respectively. If 37 balls were painted red, how many total balls are there? Correct Answer 60

GIVEN :

Balls are divided into two parts in the ratio 2 ∶ 1.

The balls in the first part are further divided in ratio 4 ∶ 1 and painted red and yellow respectively.

The balls from the second part are divided in the ratio 1 ∶ 3 and painted red and green respectively.

If 37 balls were painted red.

 

ASSUMPTION :

Let the total no. of balls be ‘x’

 

CALCULATION :

No. of balls in first part = (2/3)x

No. of balls painted red in first part = (4/5) × (2/3)x = (8/15)x

No. of balls in second part = (1/3)x

No. of balls painted red in second part = (1/4) × (1/3)x = (1/12)x

Hence, total no. of balls painted red = (8/15)x + (1/12)x = 37

⇒ (37/60)x = 37

⇒ x = 60

∴ Total no. of balls are 60

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