BITSAT 2024 Shift 1 Paper

Let's denote Bishnu's current age by $B$ and Anil's current age by $A$.We are given:The product of their ages is 240 :$A \times B = 240.$Twice Bishnu's age is 4 years more than Anil's age:$2B = A + 4$Step 1: Express Anil's age in terms of Bishnu's age.From the second equation,$A = 2B - 4$Step 2: Substitute this expression into the product equation.Replacing $A$ in $A \times B = 240$ gives:$(2B - 4) \times B = 240.$Step 3: Simplify and solve for $B$.Multiply out the left side:$2B^2 - 4B = 240$Divide the entire equation by 2 :$B^2 - 2B = 120$Rearrange it into standard quadratic form:$B^2 - 2B - 120 = 0$Step 4: Factor the quadratic equation.We need two numbers that multiply to -120 and add to -2 . These numbers are -12 and 10 . Hence, we factor:$(B - 12)(B + 10) = 0$Step 5: Solve for $B$.Set each factor equal to zero:$B - 12 = 0 \Rightarrow B = 12$$B + 10 = 0 \Rightarrow B = -10$Since age cannot be negative, we discard $B = -10$ and accept $B = 12$.Step 6: Find Bishnu's age 2 years ago.Bishnu's age 2 years ago is:$12 - 2 = 10$Thus, Bishnu's age 2 years ago was 10 years.The correct answer is Option A: 10 year.