Question

The profit earned by a vendor by selling bananas at a gain of 10% is ₹30 more than when he sells it a loss of 10% . Find the C.P. of bananas .​

Answer 1

Given :-

The profit earned by a vendor by selling bananas at a gain of 10% is ₹30 more than when he sells it a loss of 10% .

To find :-

The Cost Price of bananas .

Solution :-

Let the Cost Price of bananas be Rs. X

Profit on them = 10%

We know that

Selling Price = [(100+g)/100]×CP

=> SP = [(100+10)/100]×X

=> SP = (110/100)×X

=> SP = (11/10)×X

=> SP = Rs. 11X/10

and

Loss on it = 10%

We know that

Selling Price = [(100-l)/100]×CP

Selling Price = [(100-10)/100]×X

=> SP = (90/100)×X

=> SP = (9/10)×X

=> SP = Rs. 9X/10

Given that

SP at gain = SP at loss + Rs. 30

=> 11X/10 = (9X/10)+30

=> (11X/10)-(9X/10) = 30

=> (11X-9X)/10 = 30

=> 2X/10 = 30

=> X/5 = 30

=> X = 30×5

=> X = 150

Therefore, X = Rs. 150

Answer:-

The Cost Price of bananas is Rs. 150

Check :-

The CP of bananas = Rs. 150

Gain on them = 10%

We know that

SP = [(100+g)/100]×CP

=> SP = (110/100)×150

=> SP = 11×15 = Rs. 165

Loss on them = 10%

We know that

SP = [(100-l)/100]×CP

=> SP = (90/100)×150

=> SP = 9×15 = Rs. 135

The difference between two SPs

= 165-135

= Rs.30

Verified the given relations in the given problem.

Used formulae:-

♦ SP = [(100+g)/100]×CP

♦ SP = [(100-l)/100]×CP

• g = gain
• l = loss
• SP = Selling Price
• CP = Cost Price

Answer 2

Information given in question :

• The profit earned by a vendor by selling bananas at a gain of 10% is ₹30 more than when he sells it a loss of 10%

What we have to calculate :

• The cost price of bananas

Assumption :

Let the Cost price of bananas = x Rs

According to the question :

$\rm \implies \: \dfrac{110 \: x}{100} - \dfrac{90 \: x}{100} = 30 \implies \: \dfrac{20 \: x}{100} = 30$

$\rm \implies x = \dfrac{30 \times 100}{20}$

$\rm \implies x = \dfrac{3000}{20}$

$\bf \implies x =150 \: Rs$

Therefore :

$\rm \mapsto The \: cost \: price \: of \: bananas \: are \: 150 \: Rs$