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 April 1st, 2018, 08:58 AM #1 Senior Member   Joined: Aug 2014 From: India Posts: 470 Thanks: 1 How to solve this percentage problem? 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? Ans : 16(2/3)% Mixed fraction Solution : My sir wrote: (P X C) = P + (20P/100) * C - XC/100? Why did my sir consider (P X C) in calculation? Shortcut method is 100 * X/ 100 +- X I didn't understand shortcut formula also, please help. Last edited by Ganesh Ujwal; April 1st, 2018 at 09:20 AM.
 April 1st, 2018, 10:20 AM #2 Senior Member   Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 $\text {physical units consumed } = c.$ $\text {price per physical unit } = p.$ $\text {total amount expended } = t = p * c.$ Label things. If the price goes up but the total amount expended stays the same, then the physical units consumed must go down. Do you see that? So $(p + \Delta p)(c + \Delta c) = t.$ But $\Delta p = 20\% \text { of } p \implies \Delta p = 0.2p \implies (p + \Delta p) = 1.2p \implies$ $1.2p(c + \Delta c) = t \implies (c + \Delta c) = \dfrac{t}{1.2p} = \dfrac{p * c}{1.2p} = \dfrac{c}{1.2} \implies$ $\Delta c = \dfrac{c}{1.2} - c = c \left (\dfrac{1}{1.2} - 1 \right ) = c \left ( -\ \dfrac{0.2}{1.2} \right) = -\ c * \dfrac{1}{6} \implies$ $\dfrac{\Delta c}{c} = -\ \dfrac{1}{6} \approx -\ 16.67 \%.$ Do you follow that?
 April 1st, 2018, 04:05 PM #3 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,962 Thanks: 1147 Math Focus: Elementary mathematics and beyond $$p\cdot c_1=T$$ $$\frac65p\cdot c_2=T$$ Divide and rearrange... $$\frac65c_2=c_1\implies c_2=\frac56c_1$$ ,,, $c_1$ must be reduced by $\frac16$.

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