Successive Profit & Loss

Two successive transactions

If there are two successive transactions:

If the first profit/loss is x% and second profit/loss is y% (use + sign for profit and – sign for loss), then

Total profit/loss = x + y + $\frac{x y}{100}$ %

Q. Mragank bought a truck and paid 30% less than the original price. Thereafter he sold it with 10% profit on the price he had paid. The selling price is how much percent less than the original price?

Explanations :

Explanation 1: Using Traditional Method

Let original price = Rs. 100
So, the price paid by Mragank = 100 – 30% of 100 = 100 – 30 = Rs. 70

His selling price = 70 + 10% of 70 = 70 + 7 = Rs. 77

Now, our base here is the original price, i.e. Rs. 100

Required percent = 23% decrease

Explanation 2: Using Formula Method

First there is a decrease of 30% and then an increase of 10%.

Required percent = −30 + 10 − $\frac{(10) (30)}{100}$ = -20 – 3 = -23%, i.e. a decrease of 23% as compared to the original price.

More than two successive transactions

If ‘A’ sold an article to B at a profit/loss of $x_{1}$ , B sold this article to C at a profit/loss of $x_{2}$ and C sold this article to D at a profit/loss of $x_{3}$ , then cost price of the article for D is given by

CP (D) = CP(A) × $\frac{100 \pm 𝑥_{1}}{100}$ × $\frac{100 \pm 𝑥_{2}}{100}$ × $\frac{100 \pm 𝑥_{3}}{100}$

(+ve) for profit and (– ve) for loss.

Q. Anand sells a pencil to Bhaskar at a gain of 20%, who in turn sells it to Chetan at a loss of 10%. If Chetan pays Rs. 216 to Bhaskar, what must be the cost price of the pencil for Anand?

Explanations :

Explanation 1: Traditional Method

Let cost price for Anand = Rs. 100
So, selling price for Anand = cost price for Bhaskar = 100 + 20% of 100 = 100 + 20 = Rs. 120
Now, selling price for Bhaskar = cost price for Chetan = 120 - 10% of 120 = 120 - 12 = Rs. 108

But as per the question, cost price for Chetan = Rs. 216

So, the cost price for Anand must have been Rs. 200

Explanation 2: Formula Method

CP (C) = CP(A) × $\frac{100 \pm 𝑥_{1}}{100}$ × $\frac{100 \pm 𝑥_{2}}{100}$

or 216 = CP(A) × $\frac{100 + 20}{100}$ × $\frac{100 - 10}{100}$ = CP(A) × (6/5) × (9/10)

Or CP(A) = 216 × (50/54) = Rs. 200

Q. Anand sells a pencil to Bhaskar at a gain of 10%, who in turn sells it to Chetan at a gain of 9.09%. If Chetan pays Rs. 60 to Bhaskar, what must be the cost price of the pencil for Anand?

Explanations :

Explanation 1: Traditional Method

Let cost price for Anand = Rs. 100
So, selling price for Anand = cost price for Bhaskar = 100 + 10% of 100 = 100 + 10 = Rs. 110
Now, selling price for Bhaskar = cost price for Chetan = 110 + 9.09% of 110 = 110 + (110/11) = 110 + 10 = Rs. 120

But as per the question, cost price for Chetan = Rs. 60

So, the cost price for Anand must have been Rs. 50

Explanation 2: Formula Method

CP (C) = CP(A) × $\frac{100 \pm 𝑥_{1}}{100}$ × $\frac{100 \pm 𝑥_{2}}{100}$

Using the formula will lead to complex calculations, because of the second percentage 9.09%.

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Last updated on Oct 30, 2021