Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
A man ordered 4 pairs of black socks and some pairs of brown socks. The price of a black pair 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
(a)1 : 2
(b)2 : 1
(c)1 : 4
(d)4 : 1
Answer
Answer (as printed): C
Explanation
Suppose the man ordered $x$ pairs of brown socks. Let the price of a brown pair be ₹$y$. Then, price of a black pair $= ₹(2y)$. Original bill $= ₹(4 \times 2y + xy) = ₹(8y+xy)$. Changed bill $= ₹(4y + x \times 2y) = ₹(4y+2xy)$. $$\therefore (4y+2xy) = 150\% \text{ of } (8y+xy) \Leftrightarrow 4y+2xy = \frac{3}{2}(8y+xy) \Leftrightarrow 8y+4xy = 24y+3xy \Leftrightarrow xy = 16y \Leftrightarrow x = 16.$$ $\therefore$ Required ratio $= 4 : 16 = 1 : 4$.
Explanation as extracted from the printed page; notation may be imperfect.