Question

A reduction of 20% in the price of flour enables Akriti to buy an extra 5 kg of it for ₹ 320 . find (a) the original price per kg (b) the reduced price per kg​

Answer 1

Answer:

Original price is Rs.16/kg and reduced price is Rs. 12.8/kg

Step by step explanation

Let original price be Rs.x per kg

Amount of sugar can be bought of

Rs.320 = \frac{320}{x}

x= 320

Reduction =20%

New price = x-20\% = x-\frac{20}{100}=\frac{80x}{100} =\frac{4x}{5}x−20%=x−

100

20

=

100

80x =54x

New cost per kg = \frac{4x}{5}

5

4x

Now Amount of sugar can be bought of Rs.320 = \frac{320}{\frac{4x}{5}}

5

4x

320

We are given that A reduction of 20% in the price of flour enables akriti to buy an extra 5kg of it for Rs.320.

ATQ

\begin{gathered}\frac{320}{ \frac{4x}{5}} - \frac{320}{x} = 5 \\\\ \frac{1600}{4x} - \frac{320}{x }= 5 \\ \\ \frac{1600 - 1280}{4x} = 5 \\\\ \frac{320}{4x} = 5\\ \\ x = 16\end{gathered}

5

4x

320

−

x

320

=5

4x

1600

−

x

320

=5

4x

1600−1280

=5

4x

320

=5

x=16

Original price =Rs.16/kg

Reduced price=\frac{4 \times 16 }{5}

5

4×16

=Rs. 12.8/kg

Hence Original price is Rs.16/kg and reduced price is Rs.12.8