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 ?
A. Rs. 4, Rs. 23
B. Rs. 13, Rs. 17
C. Rs. 15, Rs. 14
D. Rs. 17, Rs. 13
Answers
Answer:
Option B is correct.
Step-by-step explanation:
Given that-
Let x be the fares of A to B and y be the fares of A to C.
According to questions-
2x + 3y = 77 ---------------- 1
3x + 2y = 73 ---------------- 2
Multiply in equation 1 by 2 and multiply in equation 2 by 3
2(2x + 3y = 77)
3(3x + 2y = 73)
So, 4x + 6y = 154
9x + 6y = 219
Subtracting
4x - 9x = 154 - 219
-5x = -65
x = 13 Rs
Put x = 13 in equation 1
2x + 3y = 77
2(13) + 3y =77
26 + 3y = 77
3y = 77 - 26
3y = 51
y = 17
Hence the fare for city A to b is 13 Rs and the fare for A to C is 17 Rs.
Option B is correct.
Answer:
let the fare from city A to B be x
let the fare from city A to C be y
=> 2x + 3y = 77 -------------(1)
=> 3x + 2y = 73 -------------(2)
* multiply (1) with 3 and (2) with 2
*now solving (1) and (2) by subtracting (1) from (2).
6x + 9y = 231
- 6x - 4y = -146
--------------------------
0 + 5y = 85
--------------------------
=> 5y = 85
y = 85/5
y = 17
=> 2x + 3y = 77
2x + 3(17) = 77
2x + 51 = 77
2x = 77 - 51
2x = 26
x = 26/2
x = 13
=>Therefore the bus fare will be B. Rs.13 , Rs17.
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