Q) Read the following text carefully and answer the questions that follow:

Lokesh, a production manager in Mumbai, hires a taxi everyday to go to his office. The taxi charges in Mumbai consists of a fixed charges together with the charges for the distance covered. His office is at a distance of 10 km from his home.
For a distance of 10 km to his office, Lokesh paid ₹ 105. While coming back home, he took another route. He covered a distance of 15 km and the charges paid by him were ₹ 155.
i. What are the fixed charges?
ii. What are the charges per km?
iii. If fixed charges are ₹ 20 and charges per km are ₹ 10, then how much Lokesh have to pay for travelling a distance of 10 km?
iv. Find the total amount paid by Lokesh for travelling 10 km from home to office and 25 km from office to home.
[Fixed charges and charges per km are as in (i) & (ii)]

Ans:

1. Fixed charges:

Step 1: Let’s consider that the fixed charge is X and running charge is Y,

therefore the charges for A km, charges will be given by: X + A Y

Step 2: Hence in 1st condition, for 10 km travel, charges = X + 10 Y

Since it is given the charges paid for this travel is 105

∴ X + 10 Y = 105 ………. (i)

Step 3: Similarly, in 2nd condition, for 15 km, charges paid are Rs. 155

∴ X + 15 Y = 155 ………. (ii)

.Step 4: Let’s solve equation (i) and (ii) and find values of X and Y.

By deducting equation (i) from (ii), we get:

(X + 15 Y) – (X + 10 Y) = 155 – 105

∴ 15 Y – 10 Y = 50

∴ 5 Y = 50

∴ Y =

∴ Y = 10

By substituting the value of Y in equation (ii), we get:

X + 15 (10) = 155

∴ X + 150 = 155

∴ X = 5

Therefore, fixed charges are Rs. 5.

ii. Charges per km:

Since we considered Y as variable charges per km and we calculated Y = 10 above

Therefore, variable charges are Rs. 10 per km.

iii. Charges for traveling distance of 10 km:

The charges for A km = X + A Y

Here, we are given fixed charge, X = Rs. 20 and variable charge, Y = Rs. 10/ km

Therefore charges for traveling 10 km = 20 + 10 x 10 = 120

Therefore, charges for traveling distance of 10 km will be Rs. 120

iv. Total amount paid for traveling 10 km & 25 km:

The charges for A km = X + A Y

In case i and ii, we have X = 5 and Y = 10

Therefore, charges to travel 10 km = 5 + 10 x 10 = 105

and charges to travel 25 km = 5 + 25 x 10 = 255

Total amunt too travel 10 km one way and 25 km during return = 105 + 255 = 360

Therefore, the charges paid are Rs. 360.

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