1.

Exercise - 21. A man takes 5 hours 45 min. in walking to a cer-tain place and riding back. He would have gained2 hours by riding both ways. The time he wouldtake to walk both ways is:A. 11 hrs 45 minB. 3 hrs 45 minC. 7 hrs 30 minD. 7 hrs 45 min

Answer»

Distance travelled by man is not mentioned in the question, so let us take distance as x metre in order to avoid confusion.

⇒

Time taken to walk x km + Time taken to ride x km = 5 hour 45 min { According to the question - ''A man takes 5 hours 45 min. in walking to a certain place and riding back''}

⇒=545\60hour =5 3\4hour =23 \ 4hour .......{ Let us take this as equation no .1}

⇒Then ,

Time taken to ride {2× xkm] = 5 h 45 m - 2 = 3 h 45 m [ Because in the question it has been written that ''He would have gained 2 hours by riding both ways'' . so we subtract it from total time taken].

=345 \60hour =3 3\4hour =1 5\4hour..{ Let us take this as Equation 2 }

⇒By solving equation 1 and 2 we get as -{Equation 1×Equation 2}

⇒Time taken to walk 2x km+ Time taken to ride 2x km =

⇒ 23 \ 2 hrs ..[Let us take this as equation 3 }

⇒Subtract equation 3 from equation 2 -

So we get as ⇒ 23 \ 2 - 15 \ 2 = 31 \4 hrs

So we get as 7 3 \ 4 ..

⇒So the answer is 7 hrs 45 min


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