Question

How must a shop owner mix 4 types of rice worth rs 95, rs 60, rs 90 and rs 50 per kg so that he can make the mixture of these rice worth rs 80 per kg?

Answer 1

How must a shop owner mix 4 types of rice worth Rs 95, Rs 60, Rs 90 and Rs 50 per kg so that he can make the mixture of these rice worth Rs 80 per kg?

Solution:

Here the prices of sugars are 50, 60, 90 and 95.

And the mean price is 80.

Here, prices LOWER than the mean are 50 and 60. And prices HIGHER than the mean are 90 and 95.

Thus possible pairs which can give mean value of 80 are: {50, 95} and {60, 90}

Let us denote rice of Rs. 50 with r50r50, rice of Rs. 60 with r60r60, rice of Rs. 90 with r90r90 and rice of Rs. 90 with r95r95

We apply the old alligation rule to ALL (two in this case) the pairs

For the 1st pair (r50r50, r95r95)

r50:r95=−15:−30r50:r95=−15:−30

⇒r50:r95=15:30⇒r50:r95=15:30

Similarly, for the 2st pair (r60r60, r90r90)

r60:r90=−10:−20r60:r90=−10:−20

⇒r60:r90=10:20⇒r60:r90=10:20

Thus, Final ratio:

r50:r60:r90:r95=15:10:20:30r50:r60:r90:r95=15:10:20:30

⇒r50:r60:r90:r95=3:2:4:6⇒r50:r60:r90:r95=3:2:4:6

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