A collection contains ₹20, ₹10, ₹5, ₹2, and ₹1 coins, with the same number of…

Concept

When equal numbers of coins are taken from several denominations, one complete set contains one coin of each denomination. The value of one complete set is the sum of the denomination values.

If there are n coins of every denomination, then total value = n × (sum of denominations). Hence n is found by dividing the collection value by the value of one complete set.

Application

1. Let n be the number of coins of each denomination.

2. The value of one complete set is ₹20 + ₹10 + ₹5 + ₹2 + ₹1 = ₹38.

3. Since there are n such sets, the total value is ₹38n.

4. Using the given total, ₹38n = ₹570.

5. Dividing both sides by ₹38 gives n = 570 ÷ 38 = 15.

Cross-check

A denomination-wise recomputation gives 15 × ₹20 + 15 × ₹10 + 15 × ₹5 + 15 × ₹2 + 15 × ₹1 = ₹300 + ₹150 + ₹75 + ₹30 + ₹15 = ₹570.

Therefore, the number of ₹1 coins is 15.