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April 1st, 2018, 08:58 AM   #1
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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.
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April 1st, 2018, 10:20 AM   #2
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$\text {physical units consumed } = c.$

$\text {price per physical unit } = p.$

$\text {total amount expended } = t = p * c.$

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?
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April 1st, 2018, 04:05 PM   #3
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$$p\cdot c_1=T$$

$$\frac65p\cdot c_2=T$$

Divide and rearrange...

$$\frac65c_2=c_1\implies c_2=\frac56c_1$$

,,, $c_1$ must be reduced by $\frac16$.
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