in a 100 m race , a beats b by 10 m and c by 13 m . in a race of 180 m , b will beat c by :
a : b = 100 : 90 . a : c = 100 : 87 . \ inline \ fn _ jvn { \ color { black } \ therefore \ frac { b } { c } = \ left ( \ frac { b } { a } \ times \ frac { a } { c } \ right ) = \ left ( \ frac { 90 } { 100 } \ times \ frac { 100 } { 87 } \ right ) = \ frac { 30 } { 29 } } when b runs 30 m , c runs 29 m . when b runs 180 m , c runs \ inline \ fn _ jvn { \ color { black } \ left ( \ frac { 29 } { 30 } \ times 180 \ right ) m } = 174 m \ inline \ fn _ jvn { \ color { blue } \ therefore } b beats c by ( 180 - 174 ) m = 6 m . answer : d ) 6 m
subtract(180, multiply(inverse(multiply(divide(100, subtract(100, 13)), divide(subtract(100, 10), 100))), 180))