Question

From the railway station I took a rickshaw to go home. It is decided that I have to pay ₹ X for the first kilometre and for each kilometre ₹ Y for the next. For 10 kilometres the fare is ₹ 40 and for 16 kilometres fare is ₹ 58. Find the fare for the first kilometre.

Answer 1

I pay ₹ X for the first kilometre and for each kilometre ₹ Y for the next.

For 10 kilometres, the fare will be ₹ X + 9Y.

For 16 kilometres, the fare will be ₹ X + 15Y.

For 10 kilometres, the fare is ₹ 40.

∴ X + 9Y = 40   ...(i)

For 16 kilometres, the fare is ₹ 58.

X + 15Y = 58   ...(ii)

Subtracting equation (i) from (ii), we get

X + 15Y = 58
X +   9Y = 40
−      −      −     
        6Y = 18

∴ Y = `18/6`

∴ Y = 3

Substituting Y = 3 in equation (i), we get

X + 9(3) = 40

∴ X + 27 = 40

∴ X = 40 – 27

∴ X = 13

∴ The fare for the first kilometre is ₹ 13.