Sure, let's break down the transactions step-by-step to find the required values:
### Part (a) - Rajan's Transaction:
Rajan bought the book for Rs 180 and sold it to Sajan at a profit of 20%.
1. Cost Price of Rajan: Rs 180
2. Profit Percent of Rajan: 20%
To find the selling price for Sajan:
[tex]\[ \text{Selling Price of Sajan} = \text{Cost Price of Rajan} \times \left(1 + \frac{\text{Profit Percent of Rajan}}{100}\right) = 180 \times \left(1 + \frac{20}{100}\right) \][/tex]
[tex]\[ \text{Selling Price of Sajan} = 180 \times 1.20 = Rs 216 \][/tex]
#### Therefore, the cost price of Sajan is Rs 216.
### Part (b) - Sajan's Transaction:
Sajan sold the book to Nirajan at a loss of 20%.
1. Cost Price of Sajan: Rs 216
2. Loss Percent of Sajan: 20%
To find the selling price for Nirajan:
[tex]\[ \text{Selling Price of Nirajan} = \text{Cost Price of Sajan} \times \left(1 - \frac{\text{Loss Percent of Sajan}}{100}\right) = 216 \times \left(1 - \frac{20}{100}\right) \][/tex]
[tex]\[ \text{Selling Price of Nirajan} = 216 \times 0.80 = Rs 172.80 \][/tex]
#### Therefore, the cost price of Nirajan is Rs 172.80.
### Part (c) - Nirajan's Transaction:
Nirajan wants to sell the book to receive a 5% profit.
1. Cost Price of Nirajan: Rs 172.80
2. Profit Percent of Nirajan: 5%
To find the selling price for a 5% profit:
[tex]\[ \text{Selling Price for 5\% Profit} = \text{Cost Price of Nirajan} \times \left(1 + \frac{\text{Profit Percent of Nirajan}}{100}\right) = 172.80 \times \left(1 + \frac{5}{100}\right) \][/tex]
[tex]\[ \text{Selling Price for 5\% Profit} = 172.80 \times 1.05 = Rs 181.44 \][/tex]
#### Therefore, Nirajan should sell the book at Rs 181.44 to receive a 5% profit.
