Rahul and Ram have sold some wooden and plastic toys. Selling price of each wooden toy sold by Rahul and Ram is equal and total number of toys sold by Ram is 100. Selling price of each plastic toy sold by ram and rahul is equal and the selling price of each wooden toy is two times the selling price of each plastic toy. Number of plastic toys sold by Rahul is 37.5% of the wooden toys sold by him. Number of wooden toys sold by Rahul is 66$\frac{2}{3}$% that of toys sold by Ram. Number of plastic toys sold by Ram is equal to the number of wooden toys sold by Rahul.

If the selling price of each wooden toys sold is Rs 120, then find the difference between the revenue of Rahul to the revenue of Ram by selling both types of toys (Note: Ram & Rahul sold all the plastic & wooden toys).

Correct Answer: Rs. 3900

To find the difference between the revenues of Rahul and Ram, we can break down the information given in the question step-by-step:

1. Define the Selling Prices:
Let the selling price of each plastic toy be Rs. $P$.
The selling price of each wooden toy is two times the selling price of each plastic toy.
Given that the selling price of each wooden toy is Rs. 120, we can write:
$P_{\text{wooden}}=120$
$P_{\text{plastic}}=\frac{120}{2}=60$

2. Determine the Number of Toys Sold:
Let the number of wooden toys sold by Ram be ${\mathrm{Ram}}_{\text{w}}$ and the number of plastic toys sold by Ram be ${\mathrm{Ram}}_{\text{p}}$.
The total number of toys sold by Ram is 100:
${\mathrm{Ram}}_{\text{w}}+{\mathrm{Ram}}_{\text{p}}=100$
The number of wooden toys sold by Rahul is $66\frac{2}{3}\%$ (or $\frac{2}{3}$) of the wooden toys sold by Ram:
${\mathrm{Rahul}}_{\text{w}}=\frac{2}{3}{\mathrm{Ram}}_{\text{w}}$
The number of plastic toys sold by Ram is equal to the number of wooden toys sold by Rahul:
${\mathrm{Ram}}_{\text{p}}={\mathrm{Rahul}}_{\text{w}}=\frac{2}{3}{\mathrm{Ram}}_{\text{w}}$

Substitute ${\mathrm{Ram}}_{\text{p}}$ back into the total toys equation for Ram:
${\mathrm{Ram}}_{\text{w}}+\frac{2}{3}{\mathrm{Ram}}_{\text{w}}=100$
$\frac{5}{3}{\mathrm{Ram}}_{\text{w}}=100$
${\mathrm{Ram}}_{\text{w}}=\frac{100\times 3}{5}=60$

Now we can compute the rest of the toy quantities:
${\mathrm{Ram}}_{\text{p}}=100-60=40$
${\mathrm{Rahul}}_{\text{w}}={\mathrm{Ram}}_{\text{p}}=40$

The number of plastic toys sold by Rahul is $37.5\%$ (or $\frac{3}{8}$) of the wooden toys sold by him:
${\mathrm{Rahul}}_{\text{p}}=37.5\%\times 40=\frac{3}{8}\times 40=15$

3. Calculate the Revenue for Each Person:
Revenue of Rahul:
${\text{Revenue}}_{\text{Rahul}}=({\mathrm{Rahul}}_{\text{w}}\times P_{\text{wooden}})+({\mathrm{Rahul}}_{\text{p}}\times P_{\text{plastic}})$
${\text{Revenue}}_{\text{Rahul}}=(40\times 120)+(15\times 60)=4800+900=\text{Rs.}5700$

Revenue of Ram:
${\text{Revenue}}_{\text{Ram}}=({\mathrm{Ram}}_{\text{w}}\times P_{\text{wooden}})+({\mathrm{Ram}}_{\text{p}}\times P_{\text{plastic}})$
${\text{Revenue}}_{\text{Ram}}=(60\times 120)+(40\times 60)=7200+2400=\text{Rs.}9600$

4. Find the Difference in Revenue:
$\text{Difference}={\text{Revenue}}_{\text{Ram}}-{\text{Revenue}}_{\text{Rahul}}$
$\text{Difference}=9600-5700=\text{Rs.}3900$