If the selling price is doubled, the profit triples. Find the profit percent

A. 50%

B. 70%

C. 100%

D. 120%

### Check Answer

The correct answer is (C)

p = SP – CP ⇒ (1)

It is given in the problem that on doubling the selling price, the profit triples, we have,

3p = 2SP – CP ⇒ (2)

Now, we need to find the profit percent given by

\frac{S p-C p}{C p} \times 100

We need to find SP in terms of CP to find the profit percent. We use equations (1) and (2) and solve them to find SP in terms of CP. Firstly, we subtract (1) from (2),

we get ⇒ 3p-p = SP

2p = SP ⇒ (A)

Putting this in (1), we get,

p = 2p – CP

p = CP ⇒ (B)

From (A) and (B), we get that SP = 2CP. Now, we put this in the formula of profit percentage given by

\frac{S p-C p}{C p} \times 100

We get,

\frac{2C p-C p}{C p} \times 100

**100%****Step by step Solution:**

We solve the problem by assuming that the original cost price be CP and the selling price be SP. Now, we have the profit (p), we have,p = SP – CP ⇒ (1)

It is given in the problem that on doubling the selling price, the profit triples, we have,

3p = 2SP – CP ⇒ (2)

Now, we need to find the profit percent given by

\frac{S p-C p}{C p} \times 100

We need to find SP in terms of CP to find the profit percent. We use equations (1) and (2) and solve them to find SP in terms of CP. Firstly, we subtract (1) from (2),

we get ⇒ 3p-p = SP

2p = SP ⇒ (A)

Putting this in (1), we get,

p = 2p – CP

p = CP ⇒ (B)

From (A) and (B), we get that SP = 2CP. Now, we put this in the formula of profit percentage given by

\frac{S p-C p}{C p} \times 100

We get,

\frac{2C p-C p}{C p} \times 100