# A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train

**Solution:**

We will be using the concept of two-variable linear equations to solve the given question.

Let us assume the uniform speed of the train to be x km/h and the time taken to travel the given distance be t hours.

Then distance can be calculated as follows:

Distance = speed × time = xt

Thus, the distance is xt

According to the question,

**Condition 1:** When the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time.

(x + 10)(t - 2) = xt

xt - 2x + 10t - 20 = xt

- 2x + 10t = 20 ....(1)

**Condition 2:** When the train would have been slower by 10 km/h, it would have taken 3 hours more than the scheduled time.

(x - 10)(t + 3) = xt

xt + 3x - 10t - 30 = xt

3x -10t = 30 ....(2)

Adding equations (1) and (2), we obtain

- 2x + 10t + 3x -10t = 20 + 30

x = 50

Substituting x = 50 in equation (1), we obtain

- 2 × 50 + 10t = 20

- 100 + 10t = 20

10t = 120

t = 120/10

t = 12

Therefore, distance = xt = 50 × 12 = 600

Hence, the distance covered by the train is 600 km.

**☛ Check: **Class 10 Maths NCERT Solutions Chapter 3

**Video Solution:**

## A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train

Class 10 Maths NCERT Solutions Chapter 3 Exercise 3.7 Question 3

**Summary:**

A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. The distance covered by the train is 600 km.

**☛ Related Questions:**

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- In △ABC, ∠C = 3∠B = 2(∠A + ∠B) . Find the three angles.
- Draw the graphs of the equations 5x – y = 5 and 3x – y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.
- Solve the following pair of linear equations. (i) px + qy = p - q; qx - py = p + q (ii) ax + by = c; bx + ay = 1+ c (iii) x/a - y/b = 0; ax + by = a² + b² (iv) (a - b)x + (a + b) y = a² - 2ab - b²; (a + b)(x + y) = a² + b² (v) 152x - 378y = -74; - 378x + 152y = - 604

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