A shopkeeper buys three varieties of pulses at Rs 132, Rs 160 and Rs 192 per kg respectively and mixes them in the ratio 9 : 2 : 1. The marked price per kg of the blended pulses is fixed at Rs 238, the shopkeeper gives a discount equal to $$\frac{1}{\text{n}}$$​ of the marked price and still earns a profit of 40%. What is the value of n?

Correct option is B

Given:

The shopkeeper buys three varieties of pulses at Rs 132, Rs 160, Rs 192 per kg respectively.
The pulses are mixed in the ratio 9 : 2 : 1.
The marked price per kg of the blended pulses is Rs 238.
The shopkeeper gives a discount equal to $$\frac{1}{n}$$of the marked price and earns a profit of 40%

Formula Used:

Selling Price = $$\text{Marked price} \times \left( 1 - \frac{1}{n} \right)$$

Solution:

I            :              II               :             III

132       :            160              :             192

9           :              2                :              1

Total CP  = 132 $$\times$$ 9 + 160 $$\times$$ 2 +  192 $$\times$$ 1

= 1188 + 320 + 192

= 1700

Cost Price per kg = $$\frac{1700}{12}$$ = $$\frac{425}{3}$$  

Selling Price = $$\frac{425}{3} \times \frac{7}{5}$$​​

The shopkeeper gives a discount of 1n\frac{1}{n}


$$\frac{1}{n}$$​ of the marked price.​

Selling Price = 238 $$\times$$ $$\left(1 - \frac{1}{n}\right)$$

​​$$\frac{425}{3} \times \frac{7}{5}$$ = 238 $$\times$$ ​$$\left(1 - \frac{1}{n}\right)$$

$$\left(1 - \frac{1}{n}\right)$$ = $$\frac{5}{6}$$  

​$$\frac{1}{n} = \frac{1}{6}$$ 

n = 6

Thus, the correct option is (b) 6

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