A and B sell two types of items: mobiles and laptops. The total number of items sold by A and B are in the ratio 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 from selling all their items is Rs. 1200, with a profit of Rs. 60 on each item. Additionally, the mobiles sold by B are 120\% of the laptops sold by A.

Find the ratio of the sum of mobiles sold by A and laptops sold by B to the sum of laptops sold by A and mobiles sold by B.

Question

A and B sell two types of items: mobiles and laptops. The total number of items sold by A and B are in the ratio 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 from selling all their items is Rs. 1200, with a profit of Rs. 60 on each item. Additionally, the mobiles sold by B are 120\% of the laptops sold by A.

Find the ratio of the sum of mobiles sold by A and laptops sold by B to the sum of laptops sold by A and mobiles sold by B.

Accepted Answer

**Solution:**

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

2. Define variables:
   - Mobiles sold by A = $M_A$
   - Laptops sold by A = $L_A$
   - Mobiles sold by B = $M_B$
   - Laptops sold by B = $L_B$

3. Given:
   - $M_A = 5 L_B$
   - $M_B = 1.2 L_A$ (since mobiles sold by B are 120\% of laptops sold by A)
   - Total items sold by A: $M_A + L_A = 5x$
   - Total items sold by B: $M_B + L_B = 3x$

4. Substitute $M_A = 5 L_B$ and $M_B = 1.2 L_A$ into the totals:
   - For A: $5 L_B + L_A = 5x$  (Equation 1)
   - For B: $1.2 L_A + L_B = 3x$  (Equation 2)

5. Profit difference is Rs. 1200, profit per item is Rs. 60:
   - Profit by A = $$60 \times 5x = 300x$$
   - Profit by B = $$60 \times 3x = 180x$$
   - Difference = $300x - 180x = 120x = 1200$

6. Solve for $x$:
   $$$120x = 1200 \implies x = 10$$$

7. Substitute $x=10$ into equations:
   - Equation 1: $5 L_B + L_A = 50$
   - Equation 2: $1.2 L_A + L_B = 30$

8. From Equation 1, express $L_A$:
   $$L_A = 50 - 5 L_B$$

9. Substitute into Equation 2:
   $$1.2 (50 - 5 L_B) + L_B = 30$$
   $$60 - 6 L_B + L_B = 30$$
   $$60 - 5 L_B = 30$$
   $$-5 L_B = -30$$
   $$L_B = 6$$

10. Find $L_A$:
    $$L_A = 50 - 5$ \times$ 6 = 50 - 30 = 20$$

11. Calculate mobiles sold by A and B:
    - $M_A = 5 L_B = 5 $\times$ 6 = 30$
    - $M_B = 1.2 L_A = 1.2 $\times$ 20 = 24$

12. Required ratio:
    $$
    $$\frac{M_A + L_B}{L_A + M_B} = \frac{30 + 6}{20 + 24} = \frac{36}{44} = \frac{9}{11}$$
    $$

**Answer:** 9:11

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