Question

One third of goods are sold at a 15% profit. 25% of the goods are sold at a 20% profit and the rest at 20% loss. if the total profit of ₹138.50 is earned on the whole transaction. the value in good in?​

Answer 1

Given:

One-third of goods are sold at a 15% profit. 25% of the goods are sold at a 20% profit and the rest at 20% loss.

Total profit of ₹138.50

To find:

The value of goods

Solution:

Let the total goods be 300

One third, means 100 goods are sold at 15℅ profit

25℅ means 75 goods are sold at 20℅ profit

The rest, means 125 goods are 20℅ loss

Let the price of each good be Re. 1

So, now calculating the profit and loss amounts:

For 100 goods, profit is 15℅ = Rs. 115

For 75 goods, profit is 20℅ = Rs. 90

For 125 goods, loss is 20℅ = Rs. 100

So, total amount of the selling price= Rs. 305

Total cost price = Rs.300

So, the profit = Selling price- cost price = Rs. 305-300 = Rs.5

Now equating it to the real values:

Rs.5 is the profit when total amount of goods is Rs 300

Rs. 138.50 is the profit when total amount of goods is= (300/5)*138.5 = Rs. 8310

The value of the goods is Rs. 8310.

Answer 2

The value of good is rs 8310.

Step-by-step explanation:

Consider the total value of goods is x.

1/3 of total value = $\frac{x}{3}$

25% of total value = $25\%\text{ of }x=\frac{25x}{100}=\frac{x}{4}$

Rest value = $x-\frac{x}{3}-\frac{x}{4}=\frac{12x-4x-3x}{12}=\frac{5x}{12}$

There is a profit of 15%  in 1/3 value,

So, selling price of 1/3 value = (100+15)% of (x/3)

= 115% of (x/3)

$=\frac{115x}{300}$

$=\frac{23}{60}x$

Similarly, there is a profit of 20% in 25% value and 20% loss in rest value,

Selling price of 25% value = 120% of x/4

$=\frac{120x}{400}$

$=\frac{3}{10}x$

Selling price of 5x/12 value = 80% of 5x/12

$=\frac{400x}{1200}$

$=\frac{x}{3}$

Thus, total selling price = $\frac{23}{60}x+\frac{3}{10}x+\frac{x}{3}$

$=\frac{23x+18+20x}{60}$

$=\frac{61x}{60x}$

So, profit = selling price - original price

= $\frac{61x}{60}-x$

$=\frac{x}{60}$

According to the question,

$\frac{x}{60}=138.50$

$\implies x = 138.50\times 60 = 8310$

Therefore, the value of good is rs 8310.

#Learn more:

Find the CP if SP is 1000 and profit percentage 10%.

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