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 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 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 $\frac16$. Tags percentage, problem, solve Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post lqdo Elementary Math 7 June 16th, 2016 04:21 PM shunya Elementary Math 1 December 14th, 2015 10:47 PM geocg12 Elementary Math 3 October 5th, 2015 11:29 PM jaherwasim Algebra 5 November 20th, 2012 08:03 AM jb2sea Advanced Statistics 4 December 7th, 2009 02:12 PM

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