Question

(9) 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). ORs. 13, Rs. 17
(C). ORs. 15, Rs. 14
(D). ORs. 17, Rs. 13​

Answer 1

Given :

• 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.

To find :

• The fares for cities B and C from A.

Solution :

❖Let the fare of city B from city A be Rs.x and the fare of city C from city A be Rs.y

• According to first condition

✰A to B and three tickets from city A to C cost Rs77

→ 2x + 3y = 77 -----(i)

• According to second condition

✰Three tickets from city A to B and two tickets from city A to C cost Rs. 73.

→ 3x + 2y = 73 ------(ii)

Multiply (i) by 2 and (ii) by 3

• 4x + 6y = 154
• 9x + 6y = 219

Subtract both the equations

→ (4x + 6y) - (9x + 6y) = 154 - 219

→ 4x + 6y - 9x - 6y = - 65

→ 4x - 9x = - 65

→ - 5x = - 65

→ x = 65/5

→ x = 13

Put the value of y in eqⁿ (ii)

→ 3x + 2y = 73

→ 3 × 13 + 2y = 73

→ 39 + 2y = 73

→ 2y = 73 - 39

→ 2y = 34

→ y = 34/2

→ y = 17

Therefore,

• The fare of city B from city A = Rs.x = Rs.13

• The fare of city C from city A = Rs.y = Rs.17

Answer 2

Heya !

Question:-

• 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?

Given :-

• price of 2 tickets from city A to B and price of 3 tickets from city A to C together costs = 77Rs.
• Price of 3 tickets from city A to C and Price of 2 tickets from city A to C together costs = 73Rs.

To find :-

• Fares for cities B and C from A.

Solution:-

Let us assume the cost of going from A to B be XRs.

and cost of going from A to C be YRs.

according to the first condition ;

2x + 3y = 77 .................. eq. 1

according to the second condition ;

3x + 2y = 73 .................. eq. 2

by elemination method :-

• multiply the coefficient of y of eq. 1 with eq. 2
• multiply the coefficient of y of eq. 2 with eq. 1

then,

• 2(2x+3y=77) => 4x + 6y = 154 ........... eq. 3
• 3(3x+2y=73) => 9x + 6y = 219 ........... eq. 4

subtracting eq. 3 from 4.

9x + 6y = 219

4x + 6y = 154

- - -

5x = 65

therefore, X = 13 Rs.

9(13)+6y = 219

117 + 6y = 219

6y = 102

y = 17 Rs.

hence, the fares are 13 and 17Rs.

option B is right...