Question 54

# Nisha went to buy three types of stationery products, each of them were priced at Rs. 5, Rs, 2 and Rs. 1 respectively.Â  She purchased all three types of products in more than oneÂ quantity and gave Rs. 20 to the shopkeeper. Since the shopkeeper had no change with him/her;Â he/she gave Nisha three more products of price Rs. 1 each. Find out the number ofÂ products with Nisha at the end of the transaction.

Solution

Let x, y, z be the number of items purchased by Nisha of price Rs. 5, 2, 1 respectively.

5x+2y+z = 20

Since the shopkeeper had no change with him/her; he/she gave Nisha three more products of price Rs. 1 each i.e Nisha purchased items of Rs. 17

5x+2y+z =17

She purchased all three types of products in more than one quantity,Â

If she purchases three items of Rs. 5, she cannot purchase 2 items of Rs 2 and 1

So Nisha purchases 2 items of Rs. 5.

If Nisha purchases 3 items of Rs 2., then she cannot purchase more than 1 item of Rs. 1.

Hence she must have purchased 2 items of Rs. 2 and 3 items of Rs. 1.

The number of items Nisha will have at the end of the transaction = 2+2+3+3(due to no change)

= 10

D is the correct answer.

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