A boy covered a certain distance at some speed. Had he moved 4.5 kmph faster, he would have taken 1 hr less. If he had moved 3 kmph slower, he would have taken 1 hr more. What is the distance covered by the boy?

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None of these

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Solution

The correct option is E
None of these

$L e t d i s t a n c e = x k m a n d u s u a l r a t e = y k m p h T h e n, \frac{x}{y} - \frac{x}{y + 4.5} = 1 \to y (y + 4.5) = 4.5 x - - - - - (i) A l s o, \frac{x}{y - 3} - \frac{x}{y} = 1 \to y (y - 3) = 3 x - - - - - (i i) O n d i v i d i n g (i) b y (i i), w e g e t x = 90 k m$

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A boy covered a certain distance at some speed. Had he moved 4.5 kmph faster, he would have taken 1 hr less. If he had moved 3 kmph slower, he would have taken 1 hr more. What is the distance covered by the boy?

The correct option is E None of these Let distance=x km and usual rate= y kmph Then, xy−xy+4.5=1→y(y+4.5)=4.5x−−−−−(i)Also,xy−3−xy=1→y(y−3)=3x−−−−−(ii)On dividing (i) by (ii), we get x=90 km