A man ordered a length of rope by telephone from his nearest hardware shop. But when a worker in the shop brought the rope, he found that the man on the telephone had miswritten the order by interchanging feet and inches. As a result of this, the length of rope received was only 30\% of the length he had ordered. The length of the rope which the man ordered was between
(a)6 ft and $7 \frac{1}{2} \mathrm{ft}$
(b)$7 \frac{1}{2} \mathrm{ft}$ and 9 ft
(c)9 ft and $10 \frac{1}{2} \mathrm{ft}$
(d)$10 \frac{1}{2} \mathrm{ft}$ and 12 ft
Answer
Answer (as printed): C
Explanation
Suppose the man ordered $x$ feet $y$ inches of the rope. Since $x$ and $y$ represent inches in the miswritten and actual order respectively, so each one of $x$ and $y$ is less than 12. $$[\because 1 \text { feet }=12 \text { inches }]$$ Actual order $=x$ feet $y$ inches $=(12 x+y)$ inches. Miswritten order $=y$ feet $x$ inches $=(12 y+x)$ inches. $$\therefore \quad(12 y+x)=30 \% \text { of }(12 x+y)=\frac{3}{10}(12 x+y)$$
Explanation as extracted from the printed page; notation may be imperfect.