JEE Main 2026 (Online) 23rd January Morning ShiftQuestion 1
A building construction work can be completed by two masons $A$ and $B$ together in $22.5$ days. Mason $A$ alone can complete the construction work in $24$ days less than mason $B$ alone. Then mason $A$ alone will complete the construction work in :
Quadratic Equation · Miscellaneous
Solution
Concept. Rates add: if $B$ alone takes $b$ days, $A$ takes $b-24$ days. Formulas used. (1) Work per day $=\dfrac{1}{\text{days}}$; together $\dfrac1{b-24}+\dfrac1b=\dfrac1{22.5}$Step 1 - Equation. By (1), with $\frac1{22.5}=\frac2{45}$: $$45(2b-24)=2b(b-24)\ \Longrightarrow\ b^2-69b+540=0.$$ Step 2 - Solve. $(b-60)(b-9)=0$. $b=9$ would make $A$'s time negative, so $b=60$. Step 3 - Value. $A$ takes $60-24=36$ days. Answer: (A)