Question

A merchant has 4000 units of rice, part of which he sells at 15% profit, and the rest at 45% profit. He
gains 25% profit on the whole. The quantity (in units) sold at 45% profit is:​

Answer 1

The total loes is 90₹I s the profit is 2

Answer 2

Given,

$4000$ units of rice.

Some units of rice are sold at a profit of $15$% and the rest is sold at a profit of $45$%.

The overall profit from selling $4000$ units of rice is $25$%.

To Find,

The number of units of rice sold at a profit of $45$%.

Solution,

Let the cost price of 1 unit of rice = $x$

Let "$t$"  no of units of rice is sold at a profit of 15%

Thus  "$(4000 - t)$" no units of rice are sold at a profit of 45%

The selling price of "$t$" units of rice = $(x)(t)(\frac{115}{100})$

Similarly the selling price of $(4000 - t)$ = $(x)(4000 - t)(\frac{145}{100})$

Thus the total selling price of $4000$ units of rice = $(x)(4000 - t)(\frac{145}{100}) + (x)(t)(\frac{115}{100})$

The actual cost price of $4000$ units of rice = $4000x$

Since the merchant had gained 25% from the sale of rice,

⇒ $4000x(\frac{125}{100}) = (x)(4000 - t)(\frac{145}{100}) + (x)(t)(\frac{115}{100})$

⇒ $125$×$4000$ $= 4000$×$145$ $- 145t + 115t$

⇒ $30t = 4000(145-125)$

⇒ $t = \frac{(400)(20)}{3} = 2666.67$

Thus the number of units, that the merchants sell at a profit of $15$% is $2666.67$ units.

Thus the number of units, that the merchant sells at a profit of $45$% = $4000 - 2666.67 = 1333.33$

Henceforth, the number of units of rice sold at $45$% profit is $1333.33$ units.