Radius of a circular track is 68m. 2 cyclists raj and ravi start together from the same position,at the same time and in the same direction with speed 33m/min and 44m/min. after how many minutes they meet again at the starting point.

Asked by seeni2005 | 13th Sep, 2016, 01:56: PM

Expert Answer:

begin mathsize 12px style Radius space of space the space circular space track space equals space 68 space straight m
Circumference space of space the space circular space track equals 2 πr equals 2 cross times 22 over 7 cross times 68 equals 2992 over 7 space straight m
The space speed space of space raj space and space Ravi space is space 33 space straight m divided by min space and space 44 space straight m divided by min space respectively.
So comma space the space time space taken space by space Raj space to space complete space 1 space round space of space the space circular space track equals fraction numerator 2992 over 7 over denominator 33 end fraction equals fraction numerator 2992 over denominator 7 cross times 33 end fraction equals 272 over 21 space mins
and space space the space time space taken space by space Ravij space to space complete space 1 space round space of space the space circular space track equals fraction numerator 2992 over 7 over denominator 44 end fraction equals fraction numerator 2992 over denominator 7 cross times 44 end fraction equals 272 over 28 space mins
The space time space after space which space they space meet space again space at space the space starting space point equals HCF open parentheses 272 over 21 comma 272 over 28 close parentheses
Now comma space HCF open parentheses 272 over 21 comma 272 over 28 close parentheses equals fraction numerator HCF space of space the space numerators over denominator LCM space of space the space denominators end fraction equals fraction numerator HCF left parenthesis 272 comma 272 right parenthesis over denominator LCM left parenthesis 21 comma 28 right parenthesis end fraction equals 272 over 7 space mins
So comma space the space time space after space which space they space meet space again space at space the space starting space point space is space after space 272 over 7 space mins space or space approximately space 38.86 space mins. end style

Answered by Rebecca Fernandes | 14th Sep, 2016, 10:16: AM