Read the information and answer the following questions.

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.

Find the ratio of dot pens sold on Tuesday to gel pen sold on Wednesday.

The correct option is 15:4.

Let us find the number of dot pens sold on each of the four days: Sunday, Monday, Tuesday, and Wednesday.

We are given:
- Sunday dot pens = 25
- Wednesday dot pens = 100
- Total dot pens sold in all four days = 250

Let the number of dot pens sold on Monday be $M$ and on Tuesday be $T$.
Since Tuesday's sales are 50% more than Monday's sales, we have:

$T=1.5M$

The sum of the dot pens sold on all four days is:

$25+M+T+100=250$

Simplifying the equation:

$M+T=250-125$

$M+T=125$

Substitute $T=1.5M$ into the equation:

$M+1.5M=125$

$2.5M=125$

$M=\frac{125}{2.5}=50$

Now, we can find the number of dot pens sold on Tuesday ($T$):

$T=1.5\times 50=75$

Next, we analyze the gel pens. We are given:
- Total gel pens sold on these four days = 50
- The number of gel pens sold on each day is Y% less than the dot pens sold on that day.

This means for any day:
$\text{Gel pens sold}=\text{Dot pens sold}\times (1-\frac{Y}{100})$

Summing this over all four days gives:

$\text{Total gel pens}=\text{Total dot pens}\times (1-\frac{Y}{100})$

Substitute the total values into the equation:

$50=250\times (1-\frac{Y}{100})$

$1-\frac{Y}{100}=\frac{50}{250}=\frac{1}{5}$

So, the number of gel pens sold on any day is $\frac{1}{5}$ (or 20%) of the dot pens sold on that day.

Now, let's find the number of gel pens sold on Wednesday:

$\text{Gel pens on Wednesday}=\frac{1}{5}\times \text{Dot pens on Wednesday}$

$\text{Gel pens on Wednesday}=\frac{1}{5}\times 100=20$

Finally, we find the ratio of dot pens sold on Tuesday to gel pens sold on Wednesday:

$\text{Ratio}=\frac{\text{Dot pens on Tuesday}}{\text{Gel pens on Wednesday}}=\frac{75}{20}$

Simplifying the fraction by dividing both numerator and denominator by 5:

$\text{Ratio}=\frac{15}{4}$

Thus, the ratio is 15:4.