MAT Exam 2021 Paper

Concept:The amount of the bill remains the same in both cases, so use the present worth formula: Amount = Present worth $\times \left(1+\frac{\text{rate}\times \text{time}}{100}\right)$.Explanation:Let the amount of the bill be ₹$A$ and the rate be $R\%$ per annum.When the bill is due in 7 months, time $=\frac{7}{12}$ years.$$A = 1200\left(1+\frac{R\times \frac{7}{12}}{100}\right) = 1200 + 7R$$When the bill is due in $2\frac{1}{2}$ years, time $=\frac{5}{2}$ years.$$A = 1016\left(1+\frac{R\times \frac{5}{2}}{100}\right) = 1016 + 25.4R$$Equate the two amounts of the bill:$$1200 + 7R = 1016 + 25.4R$$$$\Rightarrow 18.4R = 184$$$$\Rightarrow R = 10$$Answer:The rate per cent of the bill is $10\%$ per annum.Correct option: B.