Discussion
In what ratio must a grocer mix two varieties of pulses costing ₹15 and ₹20 per kg to get a mixture worth ₹16.50 per kg?
Answer: B
Correct answer: 7 : 3
By alligation the quantities are in the inverse ratio of the distances from the mean: \[ \frac{\text{cheaper}}{\text{dearer}} = \frac{20 - 16.50}{16.50 - 15} = \frac{3.50}{1.50} = \frac{7}{3}. \] The ratio is 7 : 3. Checking: 7 kg at 15 and 3 kg at 20 cost \( 105 + 60 = 165 \) for 10 kg, which is 16.50 per kg. The direction can be verified without arithmetic. The mean of 16.50 is much closer to 15 than to 20, so the cheaper variety must dominate heavily - which rules out 3 : 7 and 2 : 5 at a glance. Reversing the ratio is the commonest error in this topic, and this check catches it every time. Multiplying both differences by 2 to clear the decimals - \( 7 : 3 \) from \( 3.5 : 1.5 \) - is the practical step that keeps the arithmetic clean.
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