Two friends Samarth and Saksham went to an antique store to purchase 34 old coins of single type.
They finally short-listed coins of two types A and B and decided to choose the one having lowest price. On being asked the price, the shopkeeper told them coin 'A' is priced at Rs. 27 each and coin B is priced at Rs. 35 each. Samarth helped Saksham to select the type of coin on the basis of price. They further decided to the total amount paid by them.
Answers
Given : coin 'A' is priced at Rs. 2^7 each and coin B is priced at Rs. 3^5 each.
To Find : Type of coin which is cheaper
Final cost to purchase 3⁴ coins
Solution:
coin 'A' is priced at Rs. 2⁷ each
= 2.2⁶
= 2.(2³)²
= 2.(8)²
coin 'B' is priced at Rs. 3⁵ each
= 3.3⁴
= 3.(3²)²
= 3.(9)²
Clearly 2.(8)² < 3.(9)²
as 8 and 2 both are less than 9 and 3 respectively and powers are same
Hence 2⁷ < 3⁵
128 < 243
Coin A price of each 2⁷
Coins = 3⁴
Total Amount Paid = 2⁷ . 3⁴
= 128 * 81
= 10368
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