Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: A person who travels a certain distance to his office by his car.If he increases his speed by 8 km/hr, he takes 2 hours less time but if he drives 8 km/hr slower, he takes 4 hours more time. Find the distance of office from home. Quantity B: A person who travels a certain distance to his office by his car. If he increases his speed by 10 km/hr, he takes 1 hour less time but if he further increases his speed by 5 km/hr, he takes further 20 minutes lesser time. Find the distance of office from home. Correct Answer Quantity A > Quantity B Quantity A: Suppose ‘s’km/hr is the speed of the car and ‘D’ km is the distance; If he increases his speed by 8 km/hr, he takes 2 hours less time; ∴ D/s – D/(s + 8) = 2 ⇒ D = /8 ----(1) If he drives 8 km/hr slower, he takes 4 hours more time; ∴ D/(s – 8) – D/s = 4 ⇒ D = /8 ----(2) From equation (1) and (2); /8 = /8 ⇒ 2s + 16 = 4s – 32 ⇒ 2s = 48 ⇒ s = 24 ∴ D = /8 = 192 km Quantity B: Suppose ‘s’ km/hr is the speed of the car and ‘D’ km is the distance; If he increases his speed by 10 km/hr, he takes 1 hour less time; ∴ D/s – D/(s + 10) = 1 ⇒ D = /10 ----(1) If he further increases his speed by 5 km/hr, he takes further 20 minutes ( = 1/3 hours) lesser time; ∴ D/s – D/(s + 15) = (1 + 1/3) ⇒ D = /15 ----(2) From equation (1) and (2); /10 = /15 ⇒ 9(s + 10) = 8(s + 15) ⇒ 9s + 90 = 8s + 120 ⇒ s = 30 ∴ D = /10 = 120 km ∴ Quantity A > Quantity B