Question

Tickets to a concert cost either Rs. $4$ or Rs. $3$. A total of $400$ tickets are sold, and the total receipts were Rs. $1,380$. How many of each kind of ticket were sold?

• A. $180$ and $220$
• B. $180$ and $200$
• C. $200$ and $190$
• D. $220$ and $190$

Answer 1

Answer: (A)

$180$ and $220$

Let the number of tickets be $x$ and $y$
Then the first equation becomes,
$x+y=400$ .....(1)
$4x+3y=1,380$ ....(2)
Multiply the equation (1) by $4$ and then subtract the equations,
$4x+4y=1,600$
$4x+3y=1,380$
_______________
$y=220$
Put the value of $y$ in equation (1)
$x+y=400$
$\Rightarrow x=400220$
$\Rightarrow x=180$
There were $180$ tickets sold for Rs. $4$ each and $220$ tickets sold for Rs. $3$ each.