Rohit covers a certain distance by car. If he had increased his speed by 10 km/h, then he would have saved 2 hrs. But if he had decreased his speed by 20 km/h, then he would have taken 5 hrs more. What is the total distance covered?

## Answer

Correct Answer : a ) 4200 km

Explanation :According to the question,

Let the normal speed be x km/h

If he had increased his speed by 10 km/h then he would have saved 2 hrs

We know that, If the same distance is travelled at two different speeds and the difference between the time taken in both cases is known then we can use the formula written below directly

D=\(S_1Ã—S_2 \over S_1-S_2\)(Difference in time)

Where D, S_{1} and S_{2} are Distance, Normal speed, Increased or decreased speed

Substituting the values

⇒ \(D={{x (x+ 10)} \over { x+10-x}}*2\)

⇒\({{x (x+ 10)} \over 10}*2\)

⇒\({{x (x+ 10)} \over 15}\)…………1

If he had decreased his speed by 20 km/h, then he would have taken 5 hrs more

⇒D=\({{x (x - 20)} \over {x-x+20} } *5\)

⇒D=\({{x (x - 20)} \over {20} } *5\)…….2

Equating (1) and (2)

⇒\({{x (x + 10)} \over 5}={ {x(x-20)} \over 20 } *5\)

⇒ 4(x + 10) = 5(x – 20)

⇒ 4x + 40 = 5x – 100

⇒ x = 140 km/h

Substituting the value of x in eq (1)

D=\({{x (x +10)} \over 5} \)

⇒D=\({{140 *(140 + 10)} \over {5} }\)

⇒ D = 4200 km

Hence, (a) is the correct answer.

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