A shop sells two types of pens dot and gel in four given days. Sunday: Total number of dot pens sold is 25. Monday: dot pens sold are X% more than that on Sunday. Tuesday: dot pen sold are 50% more than that on Monday. Wednesday: total dot pens sold 100. Total number of dot pens sold in all four days are 250 and total number of gel pens sold on these four days are Y% less than dot pens sold on each day. Total gel pens are 50.

If the cost of each gel pens is Rs 5 and cost of each dot pens is Rs 10. Find the revenue generated by selling all the pens on Tuesday.

To find the revenue generated by selling all the pens on Tuesday, we need to determine the number of dot pens and gel pens sold on Tuesday.

Step 1: Understand the dot pens sold on each day
Let the number of dot pens sold on Sunday, Monday, Tuesday, and Wednesday be $D_{\mathrm{Sun}}$, $D_{\mathrm{Mon}}$, $D_{\mathrm{Tue}}$, and $D_{\mathrm{Wed}}$ respectively.
We are given:
- Sunday: $D_{\mathrm{Sun}}=25$
- Monday: $D_{\mathrm{Mon}}=25(1+\frac{X}{100})$
- Tuesday: $D_{\mathrm{Tue}}=1.5\times D_{\mathrm{Mon}}$ (50% more than Monday)
- Wednesday: $D_{\mathrm{Wed}}=100$
- Total dot pens sold in all four days = 250

Using the total sum of dot pens:
$D_{\mathrm{Sun}}+D_{\mathrm{Mon}}+D_{\mathrm{Tue}}+D_{\mathrm{Wed}}=250$
Substituting the known values:
$25+D_{\mathrm{Mon}}+1.5\times D_{\mathrm{Mon}}+100=250$
$125+2.5\times D_{\mathrm{Mon}}=250$
$2.5\times D_{\mathrm{Mon}}=125$
$D_{\mathrm{Mon}}=50$

Now, we can find the number of dot pens sold on Tuesday:
$D_{\mathrm{Tue}}=1.5\times 50=75$

Step 2: Find the gel pens sold on Tuesday
We are given that the total number of gel pens sold over these four days is 50. Let the gel pens sold on each day be $G_{\mathrm{Sun}}$, $G_{\mathrm{Mon}}$, $G_{\mathrm{Tue}}$, and $G_{\mathrm{Wed}}$ respectively.
The gel pens sold on these four days are Y% less than the dot pens sold on each corresponding day. This means:
$G_{\mathrm{day}}=D_{\mathrm{day}}\times (1-\frac{Y}{100})$

Summing this over all four days:
$\sum G_{\mathrm{day}}=(1-\frac{Y}{100})\times \sum D_{\mathrm{day}}$
$50=(1-\frac{Y}{100})\times 250$
$1-\frac{Y}{100}=\frac{50}{250}=\frac{1}{5}=0.2$

Thus, the number of gel pens sold on any day is $0.2$ times (or 20% of) the dot pens sold on that day.
For Tuesday:
$G_{\mathrm{Tue}}=0.2\times D_{\mathrm{Tue}}=0.2\times 75=15$

Step 3: Calculate the revenue generated on Tuesday
- Cost of each dot pen = Rs 10
- Cost of each gel pen = Rs 5

Revenue from Tuesday's sales:
$\mathrm{Revenue}=(D_{\mathrm{Tue}}\times 10)+(G_{\mathrm{Tue}}\times 5)$
$\mathrm{Revenue}=(75\times 10)+(15\times 5)$
$\mathrm{Revenue}=750+75=825$

Therefore, the revenue generated by selling all the pens on Tuesday is Rs 825.