Two friends Samarth and Saksham went to an antique store to purchase 3^4 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. 2^7 each and coin B is priced at Rs. 3^5 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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