Question

The speeds of 3 cars in the ratio 5:4:6. The ratio between the time taken by them to travel same distance is

• A. 10 :20 :30
• B. 12 :10 :13
• C. 15 :12 :11
• D. 12 :15 :10

Answer 1

The Correct Option is D

To find the ratio of time taken by the three cars to cover the same distance, we need to understand the relationship between speed, time, and distance. The basic formula is: 

\(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\)

Rearranging the formula gives:

\(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\)

Given that the speeds of the three cars are in the ratio 5:4:6, let's assume the speeds are 5x, 4x, and 6x for cars A, B, and C respectively.

Since the distance is the same for each car, the time taken is inversely proportional to their speeds. Thus, the time ratio can be expressed as the inverse of the speed ratio:

• Time taken by Car A: \(\frac{1}{5x}\)
• Time taken by Car B: \(\frac{1}{4x}\)
• Time taken by Car C: \(\frac{1}{6x}\)

To find the ratio of their times, we need to get rid of the denominators by multiplying by the LCM of the denominators (5, 4, and 6), which is 60x. We'll simplify the calculation of the time ratio as follows:

• Time ratio for Car A: \(\frac{60x}{5x} = 12\)
• Time ratio for Car B: \(\frac{60x}{4x} = 15\)
• Time ratio for Car C: \(\frac{60x}{6x} = 10\)

Therefore, the ratio of times taken by the cars to cover the same distance is 12:15:10.

Hence, the correct answer is: 12 : 15 : 10.

This matches the given correct answer.