200 मी की दौड़ में A, 20 मी से B को हरा देता है, जबकि B, 100 मी के दौड़ में C को 5 मी से हराता हैं। A एक किलोमीटर की दौड़ में C को कितने मीटर से हराता हैं ?
( a ) 150 m (b) 25 m (c) 100m (d) 125m
In 200 m race , A win to B by 20m while in 100m race , B win to C by 5m . Then find the distance by which A win the race to C in 1 km race ?
Answers
200 मी की दौड़ में A, 20 मी से B को हरा देता है, जबकि B, 100 मी के दौड़ में C को 5 मी से हराता हैं। A एक किलोमीटर की दौड़ में C को कितने मीटर से हराता हैं ?:
( a ) 150 m
In 200 m race , A win to B by 20m while in 100m race , B win to C by 5m . Then find the distance by which A win the race to C in 1 km race :
(a) 150m
In a 200m race,
When A has covered 200m, B has covered 180 m only [as A wins to B by 20m]
So, ratio of distances between A and B is given as :
A : B = 200 : 180 ......(1)
When B has covered 100m, C has covered 95 m only [as B wins to C by 5m]
So, in a 200m race, the distance between B and C would increase to twice as the length of the race is made twice i.e from 100m to 200m.
Thus the difference in the distances between B and C is 10m in a 200m race.
So, overall, in a 200m race, when A covers 200m, B will cover 180m [as stated in (1)] and C will cover 170m as the differences in the distance between B and C in a 200m race is 10m.
So, ratio of the distances between B and C is given as :
B : C = 180 : 170. ......(2)
As we required to find the relation between A and C, we need to find A : C.
So A : C = (A : B) × (B : C)
= (200/180) × (180/170) [From (1) and (2)]
= (200/170)
= 20 : 17
It means that if A covers 20m, C will cover 17m.
Similarly if A covers (20 × 50)m, C will cover (17 × 50)m.
It means that if A covers 1000m (1km), C will cover 850m.
Thus the differences in the distances between A and C when A reaches 1km is:
(1000 - 850)m = 150m
So, A will win the race to C by 150m.
Option (a) is correct.