Question

Four persons A B C D went to hotel to take tiffin the total bill was rupees 60 A agreed to pay half of the sum of the amounts paid by the other three B agreed to pay one third of the sum of the amounts paid by the other three C agrred to pay one fourth of the sum of the amounts paid by other three how much did D pay?

Answer 1

Let A, B, C, D pays k, x, y, z Rupees respectively.

We have, k + x + y + z = 60

A agrees to pay half of the sum of money paid by the other three.

So, k = 1/2 ( x + y + z)

2k = x + y + z

We can solve for k,

k + x + y + z = 60

k + 2k = 60

3k = 60

k = 20.

B agrees to pay one third of the sum of money paid by other three.

x = 1/3 ( k + y + z)

3x = k + y + z

We can solve for x,

k + x + y + z = 60

x + ( k + y + z) = 60

x + 3x = 60

4x = 60

x = 15

C agrees to pay one fourth of the sum of money paid by the other three,

y = 1/4 ( k + x + z)

4y = k + x + z

We can solve for y,

k + x + y + z = 60

y + ( k + x + z) = 60

5y = 60

y = 12

From the equation,

x + y + z + k = 60

20 + 15 + 12 + z = 60

47 + z = 60

z = 13

Therefore, Person D pays 13 Rupees.