Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from City A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A?

Options

A. Rs. 4, Rs. 23
B. Rs. 13, Rs. 17
C. Rs. 15, Rs. 14
D. Rs. 17, Rs. 13

Answer

B

Explanation

Let the fare of city B from city A= Rs. x
and the fare of city C from city A= Rs. y.
According to the question
`2x + 3y = 77 " " ....(i) xx 3`
`3x + 2y = 73 " " ....(ii) xx 2`
or, `6x + 9 = 231 ... (iii) `
`6x + 4y = 146 ... (iv)`
Subtracting (iv) from (iii), we get
`9y - 4y = 231 – 146`.
or, `5y = 85 `or, `y = 17`.
Putting `y = 17 `in (i), we get
`2x + 3 xx 17 = 77 `
or, `2x = 77-51 = 26 `
or, `x= 13. `
Therefore, Required fare of city B from city
A= Rs. x = Rs. 13.