A man covered a certain distance at some speed. If he had moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. What is the the distance in km?	Choose the correct choice from the following answers.
A) 33	B) 37	C) 40	D) 38	E) 27

Rationale: "let the distance be x km , the speed in which he moved = v kmph time taken when moving at normal speed - time taken when moving 3 kmph faster = 40 minutes ⇒ xv − xv + 3 = 4060 ⇒ x [ 1 v − 1 v + 3 ] = 23 ⇒ x [ v + 3 − vv ( v + 3 ) ] = 23 ⇒ 2 v ( v + 3 ) = 9 x . . . . . . . . . . . . . . . . ( equation 1 ) time taken when moving 2 kmph slower - time taken when moving at normal speed = 40 minutes ⇒ xv − 2 − xv = 4060 ⇒ x [ 1 v − 2 − 1 v ] = 23 ⇒ x [ v − v + 2 v ( v − 2 ) ] = 23 ⇒ x [ 2 v ( v − 2 ) ] = 23 ⇒ x [ 1 v ( v − 2 ) ] = 13 ⇒ v ( v − 2 ) = 3 x . . . . . . . . . . . . . . . . ( equation 2 ) equation 1 equation 2 ⇒ 2 ( v + 3 ) ( v − 2 ) = 3 ⇒ 2 v + 6 = 3 v − 6 ⇒ v = 12 substituting this value of v in equation 1 ⇒ 2 × 12 × 15 = 9 x = > x = 2 × 12 × 159 = 2 × 4 × 153 = 2 × 4 × 5 = 40 hence distance = 40 km answer : c"
Answer: C