The price of rice is increased by 20%, By what percentage should the consumption be reduced so that the expenditure on rice remains the same?
My sir told me this method:
physical units consumed = $c$.
price per physical unit = $p$.
total amount expended = $t=p∗c$.
$(p + \Delta p)(c + \Delta c)$ = $t$
$\implies$ $\Delta p$ = $20\% \text { of } p$ $\implies$ $\Delta p$ = $0.2p$ $\implies$ $(p + \Delta p)$ = $1.2p$
$\implies$ $1.2p(c + \Delta c)$ = $t \implies (c + \Delta c)$ = $\dfrac{t}{1.2p}$ = $\dfrac{p * c}{1.2p} = \dfrac{c}{1.2}$
Is there any easy method to solve this problem?
Ans: 16 (2/3)% (mixed fraction)