Question : A man ordered 4 pairs of black socks and some pairs of brown socks. The price of a pair of black socks 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:
Option 1: 2 : 1
Option 2: 1 : 4
Option 3: 1 : 2
Option 4: 4 : 1
Correct Answer: 1 : 4
Solution :
Let the number of brown pairs of socks be $x$.
Assume the cost of a brown pair is Re. 1.
So, the cost of a black pair is Rs. 2.
The total price of black socks $=2×4=8$
The total price of black socks $=1×x=x$
The total price of both socks $=8+x$
According to the question,
$2x+4=\frac{150}{100}×(8+x)$
$⇒2x+4=\frac{3}{2}×(8+x)$
$⇒4x+8=24+3x$
$\therefore x=16$
$\therefore$ The ratio of the number of black and brown pairs of socks in the original order = 4 : 16 = 1 : 4
Hence, the correct answer is 1 : 4.
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