Question

Each summer season, X-mart sells shirts and trousers. Five shirts and two trousers will cost $\$370$. Three shirts and four trousers will cost $\$390$. During a particularly slow season, X-mart announces a $10\%$ discount on all shirts and trousers. What would be the cost of selling two shirts and two trousers if they were sold during this discount period?

• A. $\$99$
• B. $\$110$
• C. $\$198$
• D. $\$220$

Answer 1

The correct option is C $\$198$

Let cost of one shirt is $x$ and cost of one trouser is $y$

Given, cost $5$ shirt and $2$ trouser is $\$370$

And cost $3$ shirt and $4$ trouser is $\$390$

Then

$5x+2y=370$..........(1)

$3x+4y=390$..........(2)

Multiply equation (1) by $2$, we get

$10x+4y=740$...........(3)

Substract equation (3) with (1), we get

$-7x=-350$

$\therefore x=50$

Put the value of $x=50$ in equation (1), we get

$5\left(50\right)+2y=370$

$\Rightarrow 250+2y=370$

$\Rightarrow 2y=370-250=120$

$\Rightarrow y=60$

Then cost of shirt is $\$50$ and Cost of trouser is $\$60$

But slow season X-mart give $10\%$ discount

Then cost of one shirt $=$ $\frac{50}{100}\times 50=$45$

and cost of one trouser $=$ $\frac{60}{100}\times 60=$54$

So, cost of two shirt and two trouser in slow season $=$ $2\times 45+2\times 54=90+108=$198$.