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A reduction of 20% in the price of the sugar enables a purchaser to obtain $2\dfrac{1}{2}kg$ more for Rs 160. Find the original price per kg of the sugar.
[a] Rs 16
[b] Rs 20
[c] Rs 12
[d] Rs 24

Answer Verified Verified
Hint: Assume that the initial price of one kilogram of sugar be Rs x. Hence calculate the final price of the sugar in terms of x after the reduction by 20%. Calculate the amount of sugar the purchaser could obtain initially and finally for Rs. 160. Equate the difference of the two to be equal to $2\dfrac{1}{2}kg$. Hence form an equation in x. Solve for x and hence find the original price per kg of the sugar.

Complete step-by-step answer:

Let the original price per kg of the sugar be x.

Hence the final price per kg of the sugar $=x-20%\text{ of }x=x-0.2x=0.8x$

The amount of sugar(in Kgs) which can be purchased initially for Rs 160 $=\dfrac{160}{x}$

The amount of sugar(in kgs) which can be purchased after price reduction by 20% is $=\dfrac{160}{0.8x}=\dfrac{200}{x}$

Since finally we can purchase $2\dfrac{1}{2}kg$ of sugar more, we have

$\dfrac{200}{x}-\dfrac{160}{x}=2\dfrac{1}{2}=\dfrac{5}{2}$

Taking x as L.C.M, we get

$\dfrac{200-160}{x}=\dfrac{5}{2}\Rightarrow \dfrac{40}{x}=\dfrac{5}{2}$

Cross multiplying, we get

$5x=80$

Dividing both sides by 5, we get

$x=\dfrac{80}{5}=16$

Hence the original price of the sugar was 16/kg

Hence option [a] is correct.

Note: Verification:

Amount of sugar which can be purchased initially for Rs 160 $=\dfrac{160}{16}=10kg$

Amount of sugar which can be purchased finally for Rs 160 $=\dfrac{160}{12.8}=\dfrac{1600}{128}=\dfrac{25}{2}kg$

Hence the extra amount of sugar which can be finally purchases for Rs 160 $=\dfrac{25}{2}-10=\dfrac{5}{2}=2\dfrac{1}{2}kg$

Hence our answer is verified to be correct.