Discussion
In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
Answer: C
The alligation rule gives the ratio in which two ingredients must be mixed:
\[ \frac{\text{cheaper quantity}}{\text{dearer quantity}} = \frac{\text{dearer} - \text{mean}}{\text{mean} - \text{cheaper}} \]
\[ \frac{\text{Rs. 15 pulses}}{\text{Rs. 20 pulses}} = \frac{20 - 16.50}{16.50 - 15} = \frac{3.50}{1.50} = \frac{7}{3} \]
The mean of 16.50 lies much nearer 15, so the cheaper variety dominates - consistent with the 7 : 3 split.
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