In a 1000 m race, A beats B by 70 m and B beats C by 100 m. In the same race, by how many meters does A beat C?  Choose the correct choice
A) 145 m	B) 176 m	C) 168 m	D) 163 m	E) 218 m

Rationale: by the time a covers 1000 m , b covers ( 1000 - 70 ) = 930 m . by the time b covers 1000 m , c covers ( 1000 - 100 ) = 900 m . so , the ratio of speeds of a and c = 1000 / 930 * 1000 / 900 = 1000 / 837 so , by the time a covers 1000 m , c covers 837 m . so in 1000 m race a beats c by 1000 - 837 = 163 m . answer : d
Answer: D