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Question

# A man covers a certain distance on bike. Had he moved 4 kmph faster, he would have taken 72 minutes less. If he moves slow by 4 kmph, he will take 2 hours more to cover the distance. What is the distance traveled by him?

A
96 km
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B
40 km
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C
50 km
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D
25 km
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Solution

## The correct option is C 96 kmLet the distance travelled be d km and speed be be s km/hrTime taken if travelled at normal speed =ds hrHad he moved 4 kmph faster, he would have taken 72 minutes less⇒ds+4=ds−7260⇒ds+4=ds−65⇒d(1s+4−1s)=−65⇒d(s−s−4s(s+4))=−65⇒d(−4s(s+4))=−65⇒d(2s(s+4))=35⇒10d=3s(s+4) ............(1)If he moves slow by 4 kmph, he will take 2 hours more to cover the distance⇒ds−4=ds+2⇒ds−4−ds=2⇒d(1s−4−1s)=2⇒d(s−s+4s(s−4))=2⇒d(2s2−4s)=1⇒2d=s2−4s or ⇒2d×5=(s2−4s)×5⇒10d=5s2−20s ..........(2) Equating (1) and (2) we get⇒3s(s+4)=5s2−20s⇒3s2+12s=5s2−20s⇒3s2+12s−5s2+20s=0⇒−2s2+32s=0⇒−2s(s−16)=0∴s=16 kmph and s≠0Substituting s=16 kmph in (1) we get10d=3×16(16+4)⇒10d=3×16×20⇒d=3×16×2=96 kmHence he travelled 96 km

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