Subject: General Aptitude · Chapter: H.C.F. and L.C.M. of Numbers · Exam: · Marks: · Difficulty:
A pendulum strikes 5 times in 3 seconds and another pendulum strikes 7 times in 4 seconds. If both pendulums start striking at the same time, how many clear strikes can be listened in 1 minute?
(a)195
(b)199
(c)200
(d)205
Answer
Answer (as printed): B
Explanation
First pendulum strikes once in $\frac{3}{5}$ seconds. Second pendulum strikes once in $\frac{4}{7}$ seconds. L.C.M. of $\frac{3}{5}$ and $\frac{4}{7}=\frac{\text { L.C.M. of } 3 \text { and } 4}{\text { H.C.F. of } 5 \text { and } 7}=12$. So, they strike together after every 12 seconds. Thus, they strike together $\left(\frac{60}{12}+1\right)=6$ times in 1 minute. ∴ Total number of clear strikes heard $$\begin{aligned} & =\left[\frac{60}{\left(\frac{3}{5}\right)}+\frac{60}{\left(\frac{4}{7}\right)}\right]-6=\left(60 \times \frac{5}{3}+60 \times \frac{7}{4}\right)-6 \\ & =(100+105)-6=199 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.