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Question

From Delhi station, if we buy 2 tickets for station A and 3 tickets for station B, the total cost is Rs. 77. But if we buy 3 tickets for station A and 5 tickets for station B, the total cost is Rs. 124. What are the fares from Delhi to station A and to station B?


A
A=Rs.12;B=Rs.17
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B
A=Rs.13;B=Rs.17
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C
A=Rs.18;B=Rs.17
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D
A=Rs.19;B=Rs.17
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Solution

The correct option is B $$A = Rs. 13 ; B = Rs. 17$$

Let the cost of ticket to station $$A$$ be Rs $$ x $$ and to station $$B$$ be Rs $$ y $$.
Given that,
"if we buy $$2$$ tickets for station $$A$$ and $$3$$ tickets for station $$B$$, the total cost is $$Rs.\  77$$." 

$$\Rightarrow 2x + 3y = 77 $$ --- (1)
Also, "
if we buy $$3$$ tickets for station $$A$$ and $$5$$ tickets for station $$B$$, the total cost is $$Rs.\  124$$." 

$$\Rightarrow 3x + 5y = 124 $$ --- (2)

Multiplying equation  $$
(1) $$ by $$ 3 $$, we get, 

$$ 6x + 9y = 231 $$ ----- equation $$
(3) $$

Multiplying equation  $$
(2) $$ by $$ 2 $$, we get, 

$$ 6x + 10y = 248 $$ ----- equation $$
(4) $$

Subtracting equation $$ (3) $$ from $$ (4) $$, we get:

$$(6x+10y)-(6x+9y)=248-231$$

$$\Rightarrow y = 17 $$

Substituting $$ y = 17 $$ in the equation $$ (1) $$, we get: 

$$ 2x + 3(17) = 77$$

$$\Rightarrow x = 13 $$

Hence, the fare from Delhi to station $$A$$ is $$Rs.\ 13 $$ and to station $$B$$ is $$Rs.\  17 $$.


Mathematics

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