How much does a watch lose per day, if its hands coincide every 64 minutes? (M.B.A. 2004, 05, 06; G.B.O., 2007; Campus Recruitment, 2008, 2010)
(a)$32 \frac{8}{11}$ min.
(b)$36 \frac{5}{11}$ min.
(c)90 min.
(d)96 min.
Answer
Answer (as printed): A
Explanation
55 min. spaces are covered in 60 min. 60 min. spaces are covered in $\left(\frac{60}{55} \times 60\right) \min .=65 \frac{5}{11} \min$. Loss in 64 min. $=\left(65 \frac{5}{11}-64\right)=\frac{16}{11} \mathrm{min}$. Loss in 24 hrs $=\left(\frac{16}{11} \times \frac{1}{64} \times 24 \times 60\right) \mathrm{min}=32 \frac{8}{11} \mathrm{min}$.