To understand the concept let’s first open a shop say a local retail stationary shop. Now suppose a student shows up and wants to buy 5 gel pens worth ₹ 5 each. So, what is the profit earned by the shopkeeper in net terms and its profit percentage?

Now this ₹ 5 is the selling price, the price at which the commodity is sold to its buyer. And let ₹ 4 is the price at which the shopkeeper has bought these pens from his supplier and this price is known as Cost Price. Thus, this difference between the price at which shopkeeper buys his pen and at which it is sold is known as profit/ loss earned. Now if Selling Price > Cost Price then he will earn profit and if Selling Price < Cost Price, then he will earn loss i.e.

Therefore, Profit = Selling Price – Cost Price

= ₹ 5 – ₹4 = ₹1 per pen

And consequently, Loss = Cost Price – Selling Price.

Now profit % = (profit/ Cost price) * 100 or profit % = {(selling price – cost price)/ Cost price} *100

= 1/5 * 100 = 20%

Similarly, Loss % = (loss/ Cost price) * 100 or Loss % = {(Cost price – selling price)/ Cost price} * 100

Now suppose another customer comes to the shop and bought 2 registers worth ₹ 50 each and a pencil box from him. And this time the shopkeeper has earned 40% profit on the registers. He earned profit of ₹10 on pencil box and the profit % on pencil box is 20%. Then what is the cost price and profit on register and selling price and cost price of pencil box?

In this case, we are given S.P. = ₹ 50/ each and profit% as 40%. Let C.P. be x. Now,

Profit % = (50 – x / x) * 100

40 = (50 – x / x) * 100

4x= 500 – 10x

14x = 500

x = 35.71

Profit = 50 – 35.71

= 14.83

What if the profit of 40% is on selling price instead?

Then, Profit = profit% * S.P

= 0.4 * 50

= ₹20

C.P. = S.P. – Profit

= ₹50 – ₹20

= ₹30

Let’s now move on to calculate S.P. and C.P. of pencil box. Let C.P. of pencil box be y

Since, profit % = (profit/ Cost price) *100

20 = (10/y) *100

2y = 100

y = ₹ 50

Therefore, S.P. = ₹50 + ₹10

= ₹60

Now since not many customers showed up on the first day of shop. Therefore, to popularize the shop the shopkeeper puts up discount of 20% on all the products. The first customer shows up and bought a packet of pencil and 3 erasers and still making up the profit of 30% on both the items. Then what is the actual cost price of both the items when the pencil is marked as ₹30 and eraser ₹ 5/ each.

Now what does the underlined marked mean? Here marked means Marked Price is the price that is offered to customer before discount basically, discount is just difference between marked price and Selling price i.e. Discount = M.P. – S.P.

In this case, Discount = 0.2 * Price of packet of pencil

= 0.2 *30

= ₹ 6

Therefore, S.P = 30 – 6

= ₹ 24

And profit is 30% on C.P., assume C.P. be x. Then,

0.3 = (24 – x/x)

0.3x = 24 – x

1.3x = 24

X = 18.46

Similarly, Discount = 0.2 * Price of packet of pencil

= 0.2* 3*5

= ₹ 3

Hence, S.P. = 12

And, 0.3 = 12 – y/y

1.3y = 12

Y (C.P. of 3 eraser) = 9.23

The above method of solving questions was a direct straightforward way of finding the solution. There’s also an alternative way of doing so. Let’s now learn that alternative method but this time instead of earning profit the seller was earning the loss. Consider this situation, that the stationer sold a parker pen at a loss of 20% for ₹ 100 and a pack of colored sketch pens at loss of 15% on S.P. What is the cost price and selling price of both the articles?

First let’s find out the C.P. and S.P. parker pen,

Since loss is 20% on C.P. Then,

S.P. = 0.8 of C.P.

100 = 0.8x

100/0.8 = C.P.

125 = C.P.

For sketch pens,

Loss is 15% on S.P. Let S.P. be y and C.P. be 100

Loss = 0.15y

C.P. = 1.15 y

100 = 1.15y

100/1.15 = y

Y = ₹87

The problems explained above are rather simple and easy ones. Now let’s do some problems that are bit complex and have come up in previous year CAT exam

Problem 1:

A watch dealer incurs an expense of Rs. 150 for producing every watch. He also incurs an additional expenditure of Rs. 30,000, which is independent of the number of watches produced. If he is able to sell a watch during the season, he sells it for Rs. 250. If he fails to do so, he has to sell each watch for Rs. 100. If he is able to sell only 1,200 out of 1,500 watches he has made in the season, then he has made a profit of

a) ₹ 90000

b) ₹ 75000

c) ₹ 45000

d) ₹ 60000

This question is not basic and direct as the problems given above. This one came in CAT 2016 paper and you should expect to get this level of questions in the exam and not the ones explained above earlier. Now let’s see how to solve this problem

Here, first find out cost he has incurred to produce the watches.

Since, he made 1500 watches costing ₹ 150 each and an additional ₹ 30000 expense on them.

Thus, total Cost = (1500*150) + 30000

= ₹ 255000

Now we will calculate the revenue he earned from selling them. As, he’s able to sell 1200 watches in the season @ ₹250 each

So, the revenue earned by him during the season = ₹250 * 1200

= ₹ 300000

Also, the left over 300 pieces of clocks would have been sold by the watchmaker in off season @ 100 each.

Revenue earned through these 300 watches = 300*100

= ₹ 30000

Total Revenue = ₹ 300000 + ₹30000 = ₹330000

Profit = Revenue – Cost

= ₹ 330000 – 255000

= ₹ 75000

Problem 2:

Instead of a meter scale, a cloth merchant uses a 120cm scale while buying, but uses an 80cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage?

This question above is a special one with the faulty dealer. Here, the dealer is earning profit by using false scale.

To solve this problem, first assume that price of cloth is ₹ 1/cm

Now he’s using 120 cm scale. Therefore his C.P. = (100/120)*₹1 = 0.8333/cm

Now this merchant again uses faulty scale to sell the cloth to his customers.

He uses a scale that measures 80cm as 100cm i.e. he sells 80cm for ₹100

Now he also gives discount of 20% on the cloth.

Thus, his mark up price is ₹100/80cm

So, after deducting discount @ 20%.

S.P. = ₹ 1/cm

Therefore, his profit % = (1 – 0.8333)/0.8333 * 100

= 20%

As you can see the above problem was a bit tricky, you will face similar problems in the exam. You will get more idea of the type of questions you need to practice through past year CAT papers. This is a very important topic. Every year around 3-4 questions come in the exam on profit and loss. So, practice this topic thoroughly.

]]>To understand the concept let’s first open a shop say a local retail stationary shop. Now suppose a student shows up and wants to buy 5 gel pens worth ₹ 5 each. So, what is the profit earned by the shopkeeper in net terms and its profit percentage?

Now this ₹ 5 is the selling price, the price at which the commodity is sold to its buyer. And let ₹ 4 is the price at which the shopkeeper has bought these pens from his supplier and this price is known as Cost Price. Thus, this difference between the price at which shopkeeper buys his pen and at which it is sold is known as profit/ loss earned. Now if Selling Price > Cost Price then he will earn profit and if Selling Price < Cost Price, then he will earn loss i.e.

Therefore, Profit = Selling Price – Cost Price

= ₹ 5 – ₹4 = ₹1 per pen

And consequently, Loss = Cost Price – Selling Price.

Now profit % = (profit/ Cost price) * 100 or profit % = {(selling price – cost price)/ Cost price} *100

= 1/5 * 100 = 20%

Similarly, Loss % = (loss/ Cost price) * 100 or Loss % = {(Cost price – selling price)/ Cost price} * 100

Now suppose another customer comes to the shop and bought 2 registers worth ₹ 50 each and a pencil box from him. And this time the shopkeeper has earned 40% profit on the registers. He earned profit of ₹10 on pencil box and the profit % on pencil box is 20%. Then what is the cost price and profit on register and selling price and cost price of pencil box?

In this case, we are given S.P. = ₹ 50/ each and profit% as 40%. Let C.P. be x. Now,

Profit % = (50 – x / x) * 100

40 = (50 – x / x) * 100

4x= 500 – 10x

14x = 500

x = 35.71

Profit = 50 – 35.71

= 14.83

What if the profit of 40% is on selling price instead?

Then, Profit = profit% * S.P

= 0.4 * 50

= ₹20

C.P. = S.P. – Profit

= ₹50 – ₹20

= ₹30

Let’s now move on to calculate S.P. and C.P. of pencil box. Let C.P. of pencil box be y

Since, profit % = (profit/ Cost price) *100

20 = (10/y) *100

2y = 100

y = ₹ 50

Therefore, S.P. = ₹50 + ₹10

= ₹60

Now since not many customers showed up on the first day of shop. Therefore, to popularize the shop the shopkeeper puts up discount of 20% on all the products. The first customer shows up and bought a packet of pencil and 3 erasers and still making up the profit of 30% on both the items. Then what is the actual cost price of both the items when the pencil is marked as ₹30 and eraser ₹ 5/ each.

Now what does the underlined marked mean? Here marked means Marked Price is the price that is offered to customer before discount basically, discount is just difference between marked price and Selling price i.e. Discount = M.P. – S.P.

In this case, Discount = 0.2 * Price of packet of pencil

= 0.2 *30

= ₹ 6

Therefore, S.P = 30 – 6

= ₹ 24

And profit is 30% on C.P., assume C.P. be x. Then,

0.3 = (24 – x/x)

0.3x = 24 – x

1.3x = 24

X = 18.46

Similarly, Discount = 0.2 * Price of packet of pencil

= 0.2* 3*5

= ₹ 3

Hence, S.P. = 12

And, 0.3 = 12 – y/y

1.3y = 12

Y (C.P. of 3 eraser) = 9.23

The above method of solving questions was a direct straightforward way of finding the solution. There’s also an alternative way of doing so. Let’s now learn that alternative method but this time instead of earning profit the seller was earning the loss. Consider this situation, that the stationer sold a parker pen at a loss of 20% for ₹ 100 and a pack of colored sketch pens at loss of 15% on S.P. What is the cost price and selling price of both the articles?

First let’s find out the C.P. and S.P. parker pen,

Since loss is 20% on C.P. Then,

S.P. = 0.8 of C.P.

100 = 0.8x

100/0.8 = C.P.

125 = C.P.

For sketch pens,

Loss is 15% on S.P. Let S.P. be y and C.P. be 100

Loss = 0.15y

C.P. = 1.15 y

100 = 1.15y

100/1.15 = y

Y = ₹87

The problems explained above are rather simple and easy ones. Now let’s do some problems that are bit complex and have come up in previous year CAT exam

Problem 1:

A watch dealer incurs an expense of Rs. 150 for producing every watch. He also incurs an additional expenditure of Rs. 30,000, which is independent of the number of watches produced. If he is able to sell a watch during the season, he sells it for Rs. 250. If he fails to do so, he has to sell each watch for Rs. 100. If he is able to sell only 1,200 out of 1,500 watches he has made in the season, then he has made a profit of

a) ₹ 90000

b) ₹ 75000

c) ₹ 45000

d) ₹ 60000

This question is not basic and direct as the problems given above. This one came in CAT 2016 paper and you should expect to get this level of questions in the exam and not the ones explained above earlier. Now let’s see how to solve this problem

Here, first find out cost he has incurred to produce the watches.

Since, he made 1500 watches costing ₹ 150 each and an additional ₹ 30000 expense on them.

Thus, total Cost = (1500*150) + 30000

= ₹ 255000

Now we will calculate the revenue he earned from selling them. As, he’s able to sell 1200 watches in the season @ ₹250 each

So, the revenue earned by him during the season = ₹250 * 1200

= ₹ 300000

Also, the left over 300 pieces of clocks would have been sold by the watchmaker in off season @ 100 each.

Revenue earned through these 300 watches = 300*100

= ₹ 30000

Total Revenue = ₹ 300000 + ₹30000 = ₹330000

Profit = Revenue – Cost

= ₹ 330000 – 255000

= ₹ 75000

Problem 2:

Instead of a meter scale, a cloth merchant uses a 120cm scale while buying, but uses an 80cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage?

This question above is a special one with the faulty dealer. Here, the dealer is earning profit by using false scale.

To solve this problem, first assume that price of cloth is ₹ 1/cm

Now he’s using 120 cm scale. Therefore his C.P. = (100/120)*₹1 = 0.8333/cm

Now this merchant again uses faulty scale to sell the cloth to his customers.

He uses a scale that measures 80cm as 100cm i.e. he sells 80cm for ₹100

Now he also gives discount of 20% on the cloth.

Thus, his mark up price is ₹100/80cm

So, after deducting discount @ 20%.

S.P. = ₹ 1/cm

Therefore, his profit % = (1 – 0.8333)/0.8333 * 100

= 20%

As you can see the above problem was a bit tricky, you will face similar problems in the exam. You will get more idea of the type of questions you need to practice through past year CAT papers. This is a very important topic. Every year around 3-4 questions come in the exam on profit and loss. So, practice this topic thoroughly.

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