100% of Distance

Algebra Level pending

Sudhir has to travel from town A to town B, which is certain distance apart. 30 % 30\% of the distance was travelled by car 40 % 40 \% of the remaining by bus, 50 % 50\% of the remaining by train and he still has 210 210 km to reach town B. What is the total distance between town A and town B?

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1050 1000 1200 1100

Vignesh Rao by Vignesh Rao , 20, India

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2 solutions

Caleb Townsend
Mar 16, 2015

210 = . 5 ( . 6 ( . 7 × x ) ) ) x = 210 . 5 × . 6 × . 7 = 210 ( 210 / 1000 ) = 1000 210 = .5(.6(.7\times x))) \\ x = \frac{210}{.5\times .6\times .7} \\ = \frac{210}{(210/1000)} \\ = \boxed{1000}

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Let x x be the total distance from A A to B B . Then we have

0.3 x + 0.4 ( 0.7 x ) + 0.5 ( 0.42 x ) + 210 = x 0.3x+0.4(0.7x)+0.5(0.42x)+210=x

0.79 x + 210 = x 0.79x+210=x

0.21 x = 210 0.21x=210

x = 1000 kilometers x=1000~\text{kilometers}

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