### Question 16

SSC-CGL 2020 Mar 3 Shift 2

Two racers are running in the same direction at speeds of 100 m/min and 120 m/min. What is the length of the track if the difference between their travel times is 10 minutes?

### Solution in Short

Suppose distance is LCM(100, 120) = 3000 meters. Difference of times will be 3000/100 - 3000/120 = 5 minutes. By unitary, if difference is 10 minutes, distance should be (3000/5)x10 = 6000 m = 6km answer!

### Solution in Short Alternate

Ratio of speeds is 100 : 120, i.e, 5 : 6. If distance is same, ratio of times should be 6 : 5. Difference 6k - 5k = 10, so k = 10, so actual times 60 and 50 minutes, and actual distance 60 x 100 = 6000 answer!

NOTE: short solutions are only for very experienced students. Others should try to master the standard detailed solutions, which, though longer, are much easier to remember. Believe it or not, the toppers usually follow the longer methods!### Solution in Detail

Length of the track = $\displaystyle x$ meters

Time taken by first $\displaystyle = \frac{x}{100}$

By the second $\displaystyle = \frac{x}{120}$

Difference $\displaystyle \frac{x}{100} - \frac{x}{120} = 10$

Solving, $\displaystyle x = 6000 \text{ m }\underline{Ans}$

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