How many kg of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg so that he may, on selling the mixture at 40 paise per kg gain 25% on the outlay?

A 15 kg

B 18 kg

C 20 kg

D 24 kg

E None of these

Correct Answer: Option C

Let’s say the amount of salt to be mixed at 42 paise be x

Amount of salt at 24 paisa per kg = 25 kg

Then,

Total Cost Price = amount × price

⇒ (x × 42) + (25 × 24)

= 42x + 600 …(1)

{∵ there is x with 42paise price and 25kg with a different price of 24paise.}

Total amount of salt after mixing = (x + 25) kg

Price of mixed salt = 40 paisa

Selling Price = total amount× price of selling = (x + 25)× 40 …..(2)

Given profit% = 25%

So \(Profit\ \% = \frac{{SP - CP}}{{CP}} \times 100\)

From (1) and (2), we get

\(\Rightarrow 0.25 = \frac{{\left( {(x + 25} \right) \times 40) - \left( {42x + 600} \right)}}{{42x + 600}}\)

⇒ 40x + 1000 - 42x - 600 = .25 × (42x + 600)

⇒ 400 – 2x = 10.5x + 150

⇒ 12.5x = 250

⇒ x = 20
∴ Amount of salt to be mixed at 42 paisa rate = 20 kgs