Question

A tourist has Rs. $10,000$ with him. He calculated that he could spend Rs $x$ everyday on his holidays. He spent Rs.$(x-50)$ everyday and extended his holidays by $10$ days.Calculate $x$

Answer 1

Let his tour be initially of $y$ days.

The total amount he had $=xy=\mathrm{10000...........}\left(1\right)$.

As per the problem,

$x\times y=$ ($x-50$)($y+10$) $=10000$

$xy=x(y+10)-50(y+10)$

$xy=xy+10x-50y-500$

$10x-50y=500$

$x-5y=50$(Taking 10 common )

$x=5y+50$

Solving quadratic equations

$(5y+50)y=10000$ from $\left(1\right)$

$(y+10)y=2000$

$y^2+10y-2000=0$

$y^2+50y-40y-(50\times 40)=0$

$y(y+50)-40(y+50)=0$

$(y-40)(y+50)=0$

Since $y$ can't be negative, $y=40$

Then $x=5\left(40\right)+50=250$