An employee can claim Rs 7 per km when travelling by taxi and Rs 6 per km when using his own car. In one week he claims a total of Rs 595 for travelling 90 km in all. How many kilometres did he travel by taxi?

Introduction / Context:
This is a typical linear equations problem mixing money, distance, and two different rates of reimbursement. The employee sometimes travels by taxi and sometimes by his own car, and we know the total distance and total amount claimed. We must find how many kilometres were travelled by taxi.

Given Data / Assumptions:

- Rate for taxi travel = Rs 7 per km.
- Rate for own car travel = Rs 6 per km.
- Total distance travelled in the week = 90 km.
- Total amount claimed = Rs 595.
- Let x be the kilometres travelled by taxi and y be the kilometres travelled by own car.

Concept / Approach:
We form a system of two linear equations in two variables using the distance and money information. The first equation comes from total distance (x + y = 90). The second equation comes from total reimbursement (7 x + 6 y = 595). Solving the system gives the value of x, the distance travelled by taxi.

Step-by-Step Solution:
Let taxi distance be x km and own car distance be y km. Total distance equation: x + y = 90. (1) Total claim equation: 7 x + 6 y = 595. (2) From (1), y = 90 - x. Substitute into (2): 7 x + 6 (90 - x) = 595. Compute: 7 x + 540 - 6 x = 595. So x + 540 = 595. Thus x = 595 - 540 = 55. Therefore, he travelled 55 km by taxi.

Verification / Alternative check:
If x = 55 km by taxi, then y = 90 - 55 = 35 km by own car. Money from taxi travel = 55 * 7 = Rs 385. Money from own car travel = 35 * 6 = Rs 210. Total claim = 385 + 210 = Rs 595, which matches the given amount. This confirms that the numbers are consistent and correct.

Why Other Options Are Wrong:
35 km and 25 km: These values, if used as taxi distances, will not satisfy both the total distance and total claim equations simultaneously.
65 km: This would make taxi distance too large and require a negative distance by own car to keep the total at 90 km, which is impossible.

Common Pitfalls:
Some learners mix up which variable refers to which mode of travel and may accidentally assign Rs 7 to the own car or vice versa. Others forget to enforce the total distance equation and try to work only with the money equation, which is not sufficient. Always define your variables clearly and write both equations before solving.

Final Answer:
The employee travelled 55 km by taxi.