Mathematics

1250 persons went to see a circus-show. Each adult paid ₹ 75 and each child paid ₹ 25 for the admission ticket. Find the number of adults and number of children, if the total collection from them amounts to ₹ 61,250.

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Let there be x adults and y children.

Given,

There are total 1250 persons.

∴ x + y = 1250

⇒ x = 1250 - y …….(1)

Given,

Total collection is of ₹ 61,250.

∴ 75x + 25y = 61250 …….(2)

Substituting value of x from equation (1) in equation (2), we get :

⇒ 75(1250 - y) + 25y = 61250

⇒ 93750 - 75y + 25y = 61250

⇒ 93750 - 50y = 61250

⇒ 50y = 93750 - 61250

⇒ 50y = 32500

⇒ y = $\dfrac{32500}{50}$ = 650.

Substituting value of y in equation (1), we get :

⇒ x = 1250 - 650 = 600.

Hence, number of adults = 600 and number of children = 650.

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