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A man ordered 4 pairs of black socks and some pairs of brown socks. The price of a black sock is double that of a brown pair. While preparing the bill the clerk interchanged the number of black and brown pairs by mistake which increased the bill by 50%. The ratio of the number of black and brown pairs of socks in the original order was :
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- 2:1
- 1:4
- 1:2
- 4:1
Correct Option: B
Let us assume the number of brown socks = B
Let us assume the price of brown socks = ₹ P per pair
Then price of black socks = ₹ 2P per pair
Before interchanging the shocks the amount = amount of black shocks + amount of brown shocks
⇒ Before interchanging the shocks the total amount = 4 x 2P + B x P
⇒ Before interchanging the shocks the total amount = 8P + BP
After interchanging the shocks the total amount = amount of black shocks + amount of brown shocks
⇒ After interchanging the shocks the total amount = 4 x P + B x 2P
⇒ After interchanging the shocks the total amount = 4P + 2BP
According to question,
After interchanging the shocks the total amount = Before interchanging the shocks the amount + Before interchanging the shocks the amount x 50 %
4P + 2BP = 8P + BP + (8P + BP ) x 50%
⇒ 4P + 2BP = 8P + BP + (8P + BP ) x 50/100
⇒ 4P + 2BP = 8P + BP + (8P + BP ) x 1/2
⇒ 4P + 2BP = ( 16P + 2BP + 8P + BP ) x 1/2
⇒ (4P + 2BP) x 2 = ( 16P + 2BP + 8P + BP )
⇒ 8P + 4BP = 24P + 3BP
⇒ 8P + 4BP = 24P + 3BP
⇒ 4BP - 3BP = 24P - 8P
⇒ BP = 16P
⇒ B = 16
The ratio of the number of black and brown pairs of socks = Number of block shocks / Number of Brown Shocks
⇒ The ratio of the number of black and brown pairs of socks in the original order = 4/16 = 1/4 = 1: 4
