Question

Abhishek sold an umbrella to Gaurav at a gain of 20% and Gaurav sold the same umbrella to Mukul at a loss os 10%. If mukul paid 1080 for it, then how much did Abhishek pay for it?

Answer 1

$\huge\mathfrak {Answer:-}$

Let Abhishek pays for umbrella be $x$

So,

$Given:-$

Abhishek sold an umbrella to Gaurav at a gain of $\:20\%$

So,

Gaurav pays for umbrella

$= x + 20\% \: of \: x$

$= x + \frac{20x}{100}$

$= x + \frac{x}{5}$

$= \frac{6x}{5}$

$Also\:given:-$

Gaurav sold the umbrella to Mukul at a loss of $10\%$

So,

Mukul pays for umbrella

$= \frac{6x}{5} - 10\% \: of \: \frac{6x}{5}$

$= \frac{6x}{5} + \frac{10 \times \frac{6x}{5} }{100}$

$= \frac{6x}{5} - \frac{2 \times 6x}{100}$

$= \frac{6x}{5} - \frac{3x}{25}$

$= \frac{30x - 3x}{25}$

$= \frac{27x}{25}$

$But\:given:-$

Mukul paid $Rs. 1080$ for umbrella.

So,

$\frac{27x}{25} = 1080$

$x = 1080 \times \frac{25}{27}$

$x = 40 \times 25$

$x = 1000$

$Therefore,$

Abhishek pays for umbrella = $Rs. 1000$

$\huge{Be\:Brainly}$❤️

Answer 2

Given:

Gain to Abhishek=20%

Loss to Gaurav=10%

Amount paid by Mukul= Rs.1,080

To find:

The amount paid by Abhishek

Solution:

The amount paid by Abhishek is Rs.1,000.

We can find the amount by following the given steps-

We know that Abhishek earned a profit of 20% and Gaurav had to bear a loss of 10%.

Let the amount paid by Abhishek be Rs.X.

So, the cost price of the umbrella for Abhishek is X.

Now, Abhishek earned a profit of 20%.

So, the selling price of the umbrella= Cost price+ Profit

The selling price of umbrella =X+20% of X

=X+0.20X =1.2X

This selling price of the umbrella is the cost price of the umbrella for Gaurav and Gaurav sold it at a loss of 10%.

The cost price of the umbrella for Gaurav=1.2X

The selling price of the umbrella now=1.2X - 10% of 1.2X

=1.2X-0.12X

=1.08X

Now Mukul purchases this umbrella from Gaurav for Rs.1,080.

So, the cost price of the umbrella for Mukul is equal to the selling price after the loss to Gaurav.

The cost price of the umbrella for Mukul= 1.08X

On equating, we get

1.08X=1,080

108X/100=1080

X=1080×100/108

X=10×100

X=Rs.1000

The amount paid by Abhishek, X= Rs.1000.

Therefore, the amount paid by Abhishek is Rs.1,000.