Mixing Pulses: Finding the Correct Ratio

To find the ratio in which two types of pulses must be mixed, we use the rule of alligation. This method helps determine the proportions needed to achieve a specific average cost.

Applying the Rule of Alligation

We have two varieties of pulses with different costs:

• Cost of cheaper pulse ($C_1$) = Rs. 66 per kg
• Cost of dearer pulse ($C_2$) = Rs. 88 per kg
• Desired mean cost of mixture (M) = Rs. 76 per kg

The rule of alligation states that the ratio of the quantities is inversely proportional to the difference of their costs from the mean cost.

Calculating the Mixing Ratio

The ratio is calculated as:

Ratio = (Cost of dearer pulse - Mean cost) : (Mean cost - Cost of cheaper pulse)

Ratio = ($C_2 - M$) : ($M - C_1$)

Substitute the values:

Ratio = (88 - 76) : (76 - 66)

Ratio = 12 : 10

Simplify the ratio by dividing both parts by their greatest common divisor, which is 2:

Ratio = $\frac{12}{2} : \frac{10}{2}$

Ratio = 6 : 5

Therefore, the grocer must mix the two varieties of pulses in the ratio 6:5 to get a mixture worth Rs. 76 per kg.