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 value of X.

The correct answer/option is 100.

To find the value of $X$, we can set up an equation using the information given about the number of dot pens sold on each day.

Let's represent the number of dot pens sold on each day:

- Sunday: $25$
- Monday: $X$% more than Sunday, which is:
$25+25\times \frac{X}{100}=25(1+\frac{X}{100})$
- Tuesday: 50% more than Monday, which is:
$1.5\times 25(1+\frac{X}{100})=37.5(1+\frac{X}{100})$
- Wednesday: $100$

The total number of dot pens sold over these four days is given as 250. Therefore, we can write the equation:

$\text{Sunday}+\text{Monday}+\text{Tuesday}+\text{Wednesday}=250$

Substituting the expressions for each day:

$25+25(1+\frac{X}{100})+37.5(1+\frac{X}{100})+100=250$

Combine the constant terms and the terms containing $(1+\frac{X}{100})$:

$125+62.5(1+\frac{X}{100})=250$

Subtract 125 from both sides:

$62.5(1+\frac{X}{100})=125$

Divide both sides by 62.5:

$1+\frac{X}{100}=2$

Subtract 1 from both sides:

$\frac{X}{100}=1$

Multiply by 100:

$X=100$