Alright, let's break down the solution step-by-step.
1. Total Cost:
The total cost for 40 books is Rs. 1600.
2. Books Sold:
- Sold 10 books for Rs. 40 each:
[tex]\[
10 \times 40 = Rs. 400
\][/tex]
- Sold 15 books for Rs. 45 each:
[tex]\[
15 \times 45 = Rs. 675
\][/tex]
The total income from the books sold so far is:
[tex]\[
400 + 675 = Rs. 1075
\][/tex]
3. Remaining Books:
Out of 40 books, 25 books have been sold (10 + 15), so the remaining number of books is:
[tex]\[
40 - 25 = 15
\][/tex]
4. Desired Total Income for 15% Profit:
To achieve a 15% profit on the total cost, we calculate:
[tex]\[
1600 \times 1.15 = Rs. 1840
\][/tex]
5. Additional Income Needed:
The total income required to achieve the desired profit is Rs. 1840. The income obtained already is Rs. 1075. Thus, the additional income needed from the remaining books is:
[tex]\[
1840 - 1075 = Rs. 765
\][/tex]
6. Price per Remaining Book:
To find out the price at which each of the remaining 15 books should be sold to achieve the desired profit, we divide the additional needed income by the number of remaining books:
[tex]\[
\frac{765}{15} = Rs. 51
\][/tex]
Therefore, the shopkeeper must sell each of the remaining 15 books for Rs. 51 to achieve a 15% profit on his initial outlay.
Thus, the correct option is:
b. Rs. 51
