Question:

60 kg of certain variety of sugar at Rs 32 per kg is mixed with 48 kg of another variety of sugar and the mixture is sold at the average price of Rs 28 per kg. If there be no profit or loss due to the new sale price, then the price of the second variety of sugar is:

• A

Rs 23 per kg

• B

Rs 83 per kg

• C

Rs 43 per kg

• D

Rs 28 per kg

Posted by: C.v. A. on 12.01.2018

Answer : A. Rs 23 per kg

Total weight of sugar is 60kg+48kg = 108kg

They have mentioned average price of mixture is Rs 28 per kg, so that is 108*28=Rs 3024

And we know from data given 60kg sugar at Rs 32, so it is 60*32=Rs 1920

Rs 3024(mixture)-Rs 1920(60kg variety)= Rs 1104(48kg variety)

Rs 1104/48kg = Rs 23 per kg

If 60 kg of sugar is bought at Rs32/kg , total money spent to buy it is 60x 32= Rs1920

Assume 48 kg of sugar is bought at Rs x/kg , so that total money spent on buying it is Rs.48x

It is given that the total sugar 60 +48=108 kg is sold at Rs.28/kg, earning a net sum of 108 x 28 = Rs 3024

Since there has been no profit or loss in the deal, the total money spent in buying 108 kg of sugar should be equal to the total earnings due to its sale. Writing this in the form of an equation:

1920 + 48x = 3024

or    48x = 3024-1920=1104

or    x= 1104/48=23

Hence 48 kg of sugar was bought at Rs23/kg

Answer: A : Rs 23 per kg

This involves a simple application of Alligation.

Here the first quantity is Q1 = 60

Second quantity is Q2 = 48

First rate is R1 = 32

Second rate is R2 = x (this is to be found out)

Mean rate is Rm = 28

By alligation,

(Q1 / Q2) = (Rm - R2) / (R1 - Rm)

(60 / 48) = (28 - x) / (32 - 28)

5 / 4 = (28 - x) / 4

So 5 = 28 - x

This gives x = 23

Hence, [A]

This involves a simple application of Alligation. Here the first quantity is Q1 = 60 Second quantity is Q2 = 48 First rate is R1 = 32 Second rate is R2 = x (this is to be found out) Mean rate is Rm = 28 By alligation, (Q1 / Q2) = (Rm - R2) / (R1 - Rm) (60 / 48) = (28 - x) / (32 - 28) 5 / 4 = (28 - x) / 4 So 5 = 28 - x This gives x = 23 Hence, [A]

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