MAH-CET 2026 — Reasoning PYQ

Step 1: Set up the original numbers

Given that the ratio of $X$ and $Y$ is $3:2$. Let the common variable multiplier be $k$.

Therefore, we can write the original values as:

$$X=3k$$

$$Y=2k$$

Step 2: Apply the given changes

• $60$ is subtracted from $X⟹X_{\text{new}}=3k-60$

• $60$ is added to $Y⟹Y_{\text{new}}=2k+60$

According to the question, the new ratio becomes $18:17$:

$$\frac{3k-60}{2k+60}=\frac{18}{17}$$

Step 3: Solve for $k$ using cross-multiplication

$$17\cdot (3k-60)=18\cdot (2k+60)$$

Expand both sides:

$$51k-1020=36k+1080$$

Bring all terms with $k$ to one side and constants to the other side:

$$51k-36k=1080+1020$$

$$15k=2100$$

Divide by $15$:

$$k=\frac{2100}{15}$$

$$k=140$$

Step 4: Find the original value of $X$

The original value of $X$ is $3k$:

$$X=3\times 140=420$$