Question

Due to reduction of Rs. 2 per kg
enables a person to purchase 4 kg
more sugar by spending Rs. 16.
Find the original price of sugar.​

Answer 1

Answer:

Rs 4 per kg

Step-by-step explanation:

Let the original price per kg of sugar be P and quantity purchased at this rate for Rs 16 be Rs N

Then PxN=16 (eq-1)

And if rate is reduced by Rs 2 then the buyer will be able to buy 4 kg more sugar by paying same amount i.e. Rs 16

Then (P-2)x(N+4)=16

Or PN+4P-2N-8=16

Or PN+4P-2N=24

Putting the value of PN=16 in the above equation

16+4P-2N=24

Or 4P-2N=8

Or 2P-N=4

Or N=2P-4

Putting the value of N into (eq-1)

Px(2P-4)=16

Or 2P^2–4P-16=0

Or 2P^2–8P+4P-16=0

Or 2P(P-4) + 4(P-4)=0

Or (P-4)(2P+4)=0

So from the above equation either P=4 or P= -2

But P being cost of 1kg sugur it cannot have negative value so Value of P should be 4

So the original cost price per kg of sugar is Rs4

(Proof of correctness of answer)

At the rate of Rs 4 per kg we can puchase 4 kg sugar by Rs 16

And if cost price is reduced by Rs 2 then the new cost price per kg will be 4–2=2

So Rs 2 per kg we can buy 8 kg sugar by Rs 16, Which is 4 kg mor than original qty.)

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