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Question

A man covered a certain distance at some speed had he moved 3 km/hr faster he would have taken 40 minutes less If he had moved 2 km/hr slower he would have taken 40 minutes more The distance ( in km) is

A
35
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B
3623
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C
3712
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D
40
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Solution

The correct option is D 40Let the distance = x km and usual rate = y km/hr Then xy−xy+3=4060⇒x(y+3)−xyy(y+3)=23⇒3xy(y+3)=23⇒2y(y+3)=9x...............(i)and xy−2−xy=4060⇒xy−x(y−2)y(y−2)=23 ⇒2xy(y−2)=23⇒y(y−2)=3x...............(ii)On dividing eqn (i) by eqn (ii) we get2(y+3)y−2=3⇒2y+6=3y−6⇒y=12∴ Putting the value of y in (i) we get 2 x 12 x 15 = 9x ⇒ x = 40 km/hr

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