There are three consecutive road crossings at which traffic lights change after every 30 seconds, 40 seconds, and 50 seconds respectively. If the lights change simultaneously at 6:30:00 hours, then at what time will they again change simultaneously?
6:50:00 hours
6:45:00 hours
6:40:00 hours
6:35:00 hours
Answer: (c) 6:40:00 hoursSolution: LCM of 30, 40, and 50 is 600.Hence after every 600 seconds, lights will change simultaneously. $$ 600 \ seconds = \frac{600}{60} \ minutes $$ $$ = 10 \ minutes $$ So after 10 minutes at 6:40:00 hours, the lights will change again simultaneously.
Three men A, B, and C start to run at the same time in the same direction to run around a circular stadium. A completes a round in 160 seconds, B in 180 seconds, and C in 140 seconds, all starting from the same point. After what time will they meet again at the starting point?
168 minutes
160 minutes
158 minutes
156 minutes
Answer: (a) 168 minutesSolution: LCM of 160, 180, and 140 is 10080.Hence they will meet after 10080 seconds again at the starting point. $$ 10080 \ seconds = \frac{10080}{60} \ minutes $$ $$ = 168 \ minutes $$
What fraction must be subtracted from the sum of \(\frac{1}{5}\) and \(\frac{1}{3}\) to have an average of \(\frac{1}{9}\) of all three fractions?
\(\frac{1}{3}\)
\(\frac{1}{5}\)
\(\frac{1}{9}\)
\(\frac{1}{6}\)
Answer: (b) \(\frac{1}{5}\)Solution: Let the fraction subtracted is \(x\) then. $$ \frac{1}{5} + \frac{1}{3} - x = 3 \times \frac{1}{9} $$ $$ x = \frac{1}{5} + \frac{1}{3} - \frac{1}{3} $$ $$ x = \frac{1}{5} $$