Solving the Toy Sales Revenue Problem

Let's break down the information given in the problem step by step to find the total revenue generated by seller 'A' from selling 'wooden' toys.

Understanding the Given Information

• Selling price (SP) of wooden toy (Seller A) = SP of wooden toy (Seller B). Let this be SP_W.
• Selling price (SP) of plastic toy (Seller A) = SP of plastic toy (Seller B). Let this be SP_P.
• SP_W = 2 * SP_P for both sellers.
• SP_P sold by seller A = 130 Rs.
• Ratio of total plastic toys to total wooden toys sold by seller 'A' is 3 : 8. So, PA : WA = 3 : 8, where PA is the number of plastic toys sold by A and WA is the number of wooden toys sold by A.
• Ratio of total wooden toys sold by seller 'A' to seller 'B' is 2 : 3. So, WA : WB = 2 : 3, where WB is the number of wooden toys sold by B.
• Total number of toys sold by seller 'B' is 100. So, WB + PB = 100, where PB is the number of plastic toys sold by B.
• Number of plastic toys sold by seller 'B' is equal to the number of wooden toys sold by seller 'A'. So, PB = WA.

Calculating Selling Prices

We are given that the selling price of each plastic toy sold by seller 'A' is 130 Rs.

So, SP_P = 130 Rs.

We also know that the selling price of each wooden toy is double the selling price of each plastic toy.

SP_W = 2 * SP_P

SP_W = 2 * 130 Rs.

SP_W = 260 Rs.

Finding the Number of Toys Sold by Seller A

Let's use the ratios to find the number of toys. We have the following relationships:

• PA : WA = 3 : 8
• WA : WB = 2 : 3
• PB = WA
• WB + PB = 100

From PA : WA = 3 : 8, we can represent PA and WA in terms of a variable, say 'k'.

Let WA = 8k and PA = 3k.

Now, use the ratio WA : WB = 2 : 3.

Substitute WA = 8k:

8k : WB = 2 : 3

This means <div>$\frac{8k}{WB} = \frac{2}{3}$</div>

<div>$2 \times WB = 3 \times 8k$</div>

<div>$2 \times WB = 24k$</div>

<div>$WB = \frac{24k}{2} = 12k$</div>

So, WB = 12k.

Next, use the condition PB = WA.

Since WA = 8k, we have PB = 8k.

Finally, use the total number of toys sold by seller B: WB + PB = 100.

Substitute the expressions for WB and PB in terms of k:

12k + 8k = 100

20k = 100

<div>$k = \frac{100}{20} = 5$</div>

Now that we have the value of k, we can find the actual number of wooden toys sold by seller A (WA).

WA = 8k = 8 * 5 = 40

We can also find the other numbers for verification:

• PA = 3k = 3 * 5 = 15
• WB = 12k = 12 * 5 = 60
• PB = 8k = 8 * 5 = 40

Checking B's total toys: WB + PB = 60 + 40 = 100. This matches the given information.

Calculating Total Revenue from Wooden Toys Sold by Seller A

The total revenue from wooden toys sold by seller A is the number of wooden toys sold by A multiplied by the selling price of each wooden toy.

Total Revenue (Wooden toys by A) = WA * SP_W

Total Revenue = 40 * 260 Rs.

Total Revenue = 10400 Rs.

Summary Table of Toy Sales and Prices

The total revenue generated by seller 'A' from selling all the 'wooden' toys together is 10400 Rs.