MAH-CET 2026 — Mathematics PYQ

Method 1: Algebraic Method

1. Define the Variable:

Let the required number be $x$.

2. Set up the Equation:

According to the problem, subtracting 30% of the number from the number itself results in 35:

$$x-(30\%\text{ of }x)=35$$

3. Convert Percentage to Fraction/Decimal:

We know that $30\%=\frac{30}{100}=0.3$. Substituting this back into the equation:

$$x-0.3x=35$$

4. Solve for $x$:

$$0.7x=35$$

$$x=\frac{35}{0.7}$$

Multiply both the numerator and the denominator by 10 to eliminate the decimal:

$$x=\frac{350}{7}$$

$$x=50$$

Method 2: Percentage Unit Method (Shortcut)

• Let the original number be represented as $100\%$.

• Subtracting $30\%$ from it leaves:

  $$100\%-30\%=70\%$$

• We are given that this remaining value is equal to 35:

  $$70\%=35$$

• Find the value of $1\%$:

  $$1\%=\frac{35}{70}=\frac{1}{2}=0.5$$

• Calculate the original number ($100\%$):

  $$\text{Original Number}=100\times 0.5=50$$

Therefore, the required number is 50.