# PE 3 - Profit & Loss | Arithmetic - Profit & Loss

**PE 3 - Profit & Loss | Arithmetic - Profit & Loss**

I bought a book for Rs. 100. Then I sold it off to a friend for Rs. 150. But after a while I felt sorry that I sold it and bought it back for Rs.190. How much loss (in Rs) did I incur?

- A.
No profit no loss

- B.
50

- C.
60

- D.
40

Answer: Option D

**Explanation** :

The original cost price of the book is irrelevant.

Actual cost price of book to me is at which I bought it = Rs. 190.

Selling price of the book is = Rs.150.

Loss = CP - SP = 190 – 150 = Rs. 40

Loss = Rs. 40

Hence, option (d).

Workspace:

**Answer the next 2 questions based on the information given below: **

Ahaan, Vihaan and Riyaan run different shops selling wheat. They keep their prices same. They sold wheat for Rs. 800 per ton in February and Rs. 1200 per ton in March. Their sales were 25, 28 and 33 metric tons respectively. But their turnovers (i.e., revenues) were the same for the February-March period (Assume that all the sales are integral).

**PE 3 - Profit & Loss | Arithmetic - Profit & Loss**

The total number of such possible cases is

- A.
4

- B.
5

- C.
6

- D.
7

Answer: Option D

**Explanation** :

Let the sales for January be a, b and c tons respectively for each of them.

∴ Total sales for Jan and Feb for

Ahaan: 800 × a + 1200 × (25 - a) = 30,000 – 400a

Vihaan: 800 × b + 1200 × (28 - b) = 33,600 – 400b

Riyaan: 800 × c + 1200 × (33 - c) = 39,600 – 400c

Total sales is same for all three.

∴ 30,000 – 400a = 33,600 – 400b = 39,600 – 400c

⇒ b - a = 9 or c – b = 15

⇒ b = 9 + a and c = 24 + a

∴ Possible solutions are

∴ 7 cases are possible

Hence, option (d).

Workspace:

**PE 3 - Profit & Loss | Arithmetic - Profit & Loss**

The maximum that Riyaan can sell for Rs. 1200/ton is (in tonnage)

- A.
2

- B.
4

- C.
6

- D.
8

Answer: Option C

**Explanation** :

Consider the solution to previous question.

∴ Maximum that Riyaan can sell at Rs. 1200/ton is 6 tons.

Hence, option (c).

Workspace:

**PE 3 - Profit & Loss | Arithmetic - Profit & Loss**

A bookseller sells only three books – A, B and C – on Sundays and their Selling Price are in the ratio 4 : 5 : 6 respectively. The bookseller makes 10%, 20% and 30% profit on selling A, B and C respectively. If the bookseller made an overall profit of 20% on a Sunday when he sold at least one copy of each of the three books, then which of the following statements is definitely true regarding that day?

- A.
The number of copies of A sold was the same as the number of copies of C sold.

- B.
The number of copies of A sold was more than the number of copies of C sold.

- C.
The number of copies of A sold was less than the number of copies of C sold.

- D.
None of these

Answer: Option B

**Explanation** :

Let the Selling Price of a copy A, B and C be 4x, 5x and 6x respectively.

Let the Cost Price of a copy A, B and C be CA, CB and CC respectively.

Let the number of copies of A, B and C sold on that Sunday be a, b and c respectively.

∴ 1.1aC_{A }+ 1.2bC_{B }+ 1.3cC_{C }= 1.2(aC_{A }+ bC_{B }+ cC_{C})

⇒ aC_{A} = cC_{C}

⇒ $\frac{a}{c}=\frac{{C}_{C}}{{C}_{A}}$ = $\frac{\frac{6x}{1.3}}{\frac{4x}{1.1}}$ > 1

Hence, option (b).

Workspace:

**PE 3 - Profit & Loss | Arithmetic - Profit & Loss**

A tradesman, by means of a false balance, defrauds 10% in buying goods and 10% in selling. What % does he gain on his outlay by his dishonesty if he professes to sell the goods at cost price?

- A.
21.33%

- B.
18.75%

- C.
23.33%

- D.
22.22%

Answer: Option D

**Explanation** :

Let the CP for tradesman be Rs. 1/gm

Since he defrauds 10%, he will get 110 gms for every 100 gms he pays for.

∴ He buys 110 gms for Rs. 100.

While selling, he gives only 90 gms for every 100 gms.

So, the tradesman will give 110 gms for 110 × 100/90 = Rs. 122.22

∴ Profit % = 22.22%

Hence, option (d).

Workspace:

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