A shopkeeper buys three varieties of sugar at Rs 99, Rs 120 and Rs 144 per kg respectively and mixes them in the ratio 9 : 2 : 1. In order to earn a y% profit after giving a discount equal to a sixth of the marked price, the marked price per kg of the blended sugar is fixed at Rs 178.50. What is the value of y?

Correct option is B

Given:

Prices of three varieties of sugar:

First variety: ₹99 per kg

Second variety: ₹120 per kg

Third variety: ₹144 per kg

The mixing ratio is 9 : 2 : 1.

Marked price per kg of the blended sugar = ₹178.50.

Discount on the marked price = $$\frac{1}{6}$$​of the marked price.

The shopkeeper wants to earn a profit of y%.

Formula Used:

SP = Marked Price - Discount

Discount =  $$\frac{1}{6} \times \text{Marked Price}$$​​

SP = Marked Price - $$\frac{1}{6} \times \text{Marked Price} = \frac{5}{6} \times \text{Marked Price}$$​​

y = $$\frac{\text{Profit}}{\text{Cost Price}} \times 100$$​​

Solution:

                     A        :        B         :        C

Price →      99               120              144

Quantity → 9                  2                  1    = 12

CP = $$\frac{(9 \times 99) + (2 \times 120) + (1 \times 144)}{9 + 2 + 1}$$​​

CP = $$\frac{891 + 240 + 144}{12} = \frac{1275}{12} = ₹106.25$$​​

SP = $$\frac{5}{6} \times 178.50 = ₹148.75$$​​

Profit = 148.75 - 106.25 = ₹42.50

y = $$\frac{42.50}{106.25} \times 100 = 40\%$$​​

Thus, the correct option is (b)  40