A and B sell two types of items: mobiles and laptops. The ratio of the total items sold by A to B is $5:3$. The number of mobiles sold by A is 5 times the number of laptops sold by B. The profit difference between A and B on their total sales is Rs. 1200. The profit earned on each item is Rs. 60. The mobiles sold by B are 120\% of the laptops sold by A.

The cost price of all mobiles sold by A is Rs. 1200, and the selling price of each mobile sold by A is Rs. $p$. The selling price of each laptop sold by B is Rs. $2p$. Find the cost price of one laptop sold by B (in Rs).

Question

A and B sell two types of items: mobiles and laptops. The ratio of the total items sold by A to B is $5:3$. The number of mobiles sold by A is 5 times the number of laptops sold by B. The profit difference between A and B on their total sales is Rs. 1200. The profit earned on each item is Rs. 60. The mobiles sold by B are 120\% of the laptops sold by A.

The cost price of all mobiles sold by A is Rs. 1200, and the selling price of each mobile sold by A is Rs. $p$. The selling price of each laptop sold by B is Rs. $2p$. Find the cost price of one laptop sold by B (in Rs).

Accepted Answer

**Solution:**

1. Let the total items sold by A be $5x$ and by B be $3x$.

2. Let laptops sold by B be $y$. Then mobiles sold by A = $5y$ (given).

3. Mobiles sold by B = 120\% of laptops sold by A.
   - Let laptops sold by A be $z$.
   - Then mobiles sold by B = $1.2z$.

4. Total items sold by A = mobiles by A + laptops by A = $5y + z = 5x$.

5. Total items sold by B = mobiles by B + laptops by B = $1.2z + y = 3x$.

6. Profit on each item = Rs. 60.
   - Profit difference between A and B = Rs. 1200.
   - Profit of A - Profit of B = 1200.

7. Profit of A = $60 	imes 5x = 300x$.
   Profit of B = $60 	imes 3x = 180x$.

8. Difference: $300x - 180x = 120x = 1200 \ \Rightarrow x = 10$.

9. From step 4: $5y + z = 5x = 50$.

10. From step 5: $1.2z + y = 3x = 30$.

11. Solve the system:
    - $5y + z = 50$  (i)
    - $1.2z + y = 30$ (ii)

12. From (ii): $y = 30 - 1.2z$.

13. Substitute in (i):
    $$5(30 - 1.2z) + z = 50 \ 150 - 6z + z = 50 \ 150 - 5z = 50 \ 5z = 100 \ z = 20$$

14. Then $y = 30 - 1.2 	imes 20 = 30 - 24 = 6$.

15. Mobiles sold by A = $5y = 5 	imes 6 = 30$.

16. Cost price of all mobiles sold by A = Rs. 1200.
    - Cost price per mobile by A = $\frac{1200}{30} = 40$.

17. Selling price per mobile by A = Rs. $p$.

18. Profit per mobile by A = Selling price - Cost price = $p - 40 = 60$ (profit per item).

19. So, $p = 100$.

20. Selling price of each laptop sold by B = $2p = 2 	imes 100 = 200$.

21. Profit per laptop = Rs. 60.

22. Cost price of laptop sold by B = Selling price - Profit = $200 - 60 = 140$.

**Answer:** Rs. 140

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