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?
Explanation
Correct Option - 2
Given:
2 bus tickets from city A to B + 3 bus tickets from city A to C cost Rs.77
3 bus tickets from city A to B + 2 bus tickets from city A to C cost Rs.73
Calculation:
Let the price of a bus ticket from city A to B be Rs.x
And the price of a bus ticket from city A to C be Rs.y
⇒ 2x + 3y = 77 ------(1)
And,
⇒ 3x + 2y = 73 ------(2)
Now solve the simultaneous equations,
Multiplying 1st equation by 2 and 2nd equation by 3,
⇒ 4x + 6y = 154 ------(3)
And
⇒ 9x + 6y = 219 ------(4)
Subtracting equation 3 from equation 4,
⇒ (9x + 6y) - (4x + 6y) = 219 - 154
⇒ 9x + 6y - 4x - 6y = 65
Rs. 4, Rs. 23 1.
Rs. 13. Rs. 17 2.
Rs. 15, Rs. 14 3.
Rs. 17, Rs. 13 4.
(56)
⇒ 5x = 65
⇒ x = 65\5
⇒ x = 13
Using the above value of x in 1st equation,
⇒ 2x + 3y = 77
⇒ 2(13) + 3y = 77
⇒ 26 + 3y = 77
⇒ 3y = 77 – 26
⇒ 3y = 51
⇒ y = 51/3
⇒ y = 17
∴ The price of a bus ticket from city A to B is Rs.13
And,
The price of a bus ticket from city A to C is Rs.17
