Question

The pair of $3$ full ticket and $2$ half tickets is $Rs204$ and the pair $2$ full tickets and $3$ half ticket is $RS186$. Find the cost of pair a full ticket and a half ticket

• A. $94$
• B. $78$
• C. $86$
• D. $62$

Answer 1

The correct option is B $78$

Let the cost of 1 full ticket and a half ticket be Rs. x and Rs. y respectively.

Given that the pair of 3 full ticket and 2 half tickets is Rs204.

$3x+2y=204.....\left(1\right)$

Again given the pair 2 full tickets and 3 half ticket is RS186.

$2x+3y=186.....\left(2\right)$

Multiply ${eq}^n\left(1\right)\&\left(2\right)$ by 2 and 3 respectively.

$6x+4y=408.....\left(3\right)$

$6x+9y=558.....\left(4\right)$

Subtracting ${eq}^n\left(3\right)$ from ${eq}^n\left(4\right)$, we have

$(6x+9y)-(6x+4y)=558-408$

$\Rightarrow 6x+9y-6x-4y=558-408$

$\Rightarrow 5y=150$

$\Rightarrow y=30$

Substituting the value of x in ${eq}^n\left(2\right)$, we have

$2x+3\times 30=186$

$\Rightarrow 2x=186-90$

$\Rightarrow x=\frac{96}{2}=48$

Therefore, the cost of 1 full ticket and a half ticket is Rs. 48 and Rs. 30 respectively.

$\therefore$ cost of pair of a full ticket and a half ticket $=x+y=48+30=Rs.78$

Hence, the cost of pair of a full ticket and a half ticket is Rs. 78.