Discussion
In what ratio must a shopkeeper mix Basmati rice at ₹120 per kg with ordinary rice at ₹80 per kg so that the mixture costs ₹90 per kg?
Answer: C
Correct answer: 1 : 3
By alligation the ratio of the two quantities is the inverse ratio of their distances from the mean. Taking Basmati first: \[ \frac{\text{Basmati}}{\text{ordinary}} = \frac{90 - 80}{120 - 90} = \frac{10}{30} = \frac{1}{3}. \] The ratio is 1 : 3 - one part Basmati to three parts ordinary rice. Checking: 1 kg at 120 and 3 kg at 80 cost \( 120 + 240 = 360 \) for 4 kg, which is 90 per kg. Note carefully which difference belongs to which ingredient. The quantity of an ingredient is proportional to the distance of the mean from the other price - the differences are taken diagonally across the alligation diagram. The sanity check settles it regardless: the mean of 90 is much nearer 80 than 120, so the ordinary rice must dominate, and 3 : 1 can be rejected without calculation.
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