Question

One pendulum ticks $57$ times in $58$ seconds and another $608$ times in $609$ seconds. If they start simultaneously, find the time after which will they tick together?

• A. $\frac{211}{19}s$
• B. $\frac{1217}{19}s$
• C. $\frac{1218}{19}s$
• D. $\frac{1018}{19}s$

Answer 1

The correct option is C $\frac{1218}{19}s$

One pendulum ticks $57$ times in $58$ sec.

Another pendulum ticks $608$ times in $609$ sec.

Time gap between two consecutive ticks-

$\frac{58}{57}sec\text{and}\frac{609}{608}sec$

$\therefore$ Required time = LCM of $\frac{58}{57}\text{and}\frac{609}{608}=\frac{\text{LCM of 58 and 609}}{\text{HCF of 57 and 608}}=\frac{1218}{19}sec$