Two bus tickets from city Amb to Sunhet and three from city Amb to Dehra cost Rs. 77 but three tickets from city Amb to Sunhet and two tickets from city Amb to Dehra cost Rs. 73. What are the fares for cities Sunhet and Dehra from Amb?

Two bus tickets from city Amb to Sunhet and three from city Amb to Dehra cost Rs. 77 but three tickets from city Amb to Sunhet and two tickets from city Amb to Dehra cost Rs. 73. What are the fares for cities Sunhet and Dehra from Amb?

1. A

Rs. 4, Rs. 23

2. B

Rs. 13, Rs. 17

3. C

Rs. 15, Rs. 14

4. D

Rs. 17, Rs. 13

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Solution:

Let Rs. x be the fare of city Sunhet from city Amb and Rs. y be the fare of city Dehra from city Amb.

So, we will get the equations

Then,    $2x+3y=77\text{\hspace{0.17em}}....\text{\hspace{0.17em}}\left(i\right)$  and

$3x+2y=73\text{\hspace{0.17em}}....\text{\hspace{0.17em}}\left(ii\right)$

Multiplying (i) by 3 & (ii) by 2 & subtracting, we get: 5y = 85 or y = 17.

Putting y = 17 in (i), we get: x = 13.

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