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Standard X

Mathematics

Elimination Method of Finding Solution of a Pair of Linear Equations

Two bus ticke...

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 ?

Rs.

4

, Rs.

23

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Rs.

13

, Rs.

17

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Rs.

15

, Rs.

14

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Rs.

17

, Rs.

13

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Solution

The correct option is B Rs. $13$ , Rs. $17$
Let Rs. $x$ be the fare of city B from city A and Rs. $y$ be the fare of city C from city A.
Then,
$2 x + 3 y = 77$ ...(i)
and
$3 x + 2 y = 73$ ...(ii)
Multiplying (i) by $3$ and (ii) by $2$ and subtracting,
we get: $5 y = 85$ or $y = 17.$
Putting $y = 17$ in (i), we get: $x = 13.$

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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 ?

The correct option is B Rs. 13, Rs. 17Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A.Then, 2x+3y=77...(i) and3x+2y=73 ...(ii)Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y=85 or y=17.Putting y=17 in (i), we get:x=13.