Question

In a Mathematics quiz, 30 prizes consisting of 1st and 2nd prizes only are to be given. 1st and 2nd prizes are worth ₹ 2000 and ₹ 1000, respectively. If the total prize money is ₹ 52,000 then show that:

The number of 1st prizes are ______ and the number of 2nd prizes are ______.

Answer 1

The number of 1st prizes are 22 and the number of 2nd prizes are 8.

Explanation:

Given, the number of prizes = 30

Total prize money = ₹ 52000, 1st and 2nd prizes are worth ₹ 2000 and ₹ 1000, respectively.

From (b), 2000x + 1000(30 – x) = 52000

2x + (30 – x) = 52   ......[Dividing both sides by 1000]

x + 30 = 52 

⇒ x = 52 – 30 = 22

∴ Number of 2nd prizes = 30 – 22 = 8