A man rides at the rate of 18 km/hr, but stops for 6 min, to change horses at the end of every 7th km. The time that he will take to cover a distance of 90 km is

A man rides at the rate of 18 km/hr, but stops for 6 min, to change horses at the end of every ${7}^{th}$ km. The time that he will take to cover a distance of 90 km is

1. A

6 hrs

2. B

6 hrs 12 min

3. C

6 hrs 18 min

4. D

6 hrs 24 min

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Solution:

Solution: Total distance = 90 km

$Speed=18\text{\hspace{0.17em}\hspace{0.17em}}km/hr⇒time=\frac{90\text{\hspace{0.17em}\hspace{0.17em}}km}{18\text{\hspace{0.17em}\hspace{0.17em}}kmph}=5\text{\hspace{0.17em}\hspace{0.17em}}hrs$

No.of  stops  to change horse Integral part of $\left(\frac{90}{7}\right)$

There are 12 stops i.e all multiple of 7, less than 90

$time\text{\hspace{0.17em}\hspace{0.17em}}taken\text{\hspace{0.17em}}for\text{\hspace{0.17em}\hspace{0.17em}}every\text{\hspace{0.17em}\hspace{0.17em}}stop=12×6=72\text{\hspace{0.17em}\hspace{0.17em}mins}$$Total\text{\hspace{0.17em}\hspace{0.17em}}time=5\text{\hspace{0.17em}\hspace{0.17em}}hrs+60\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{min}+12\text{\hspace{0.17em}\hspace{0.17em}mins}=6\text{\hspace{0.17em}\hspace{0.17em}}hrs\text{\hspace{0.17em}\hspace{0.17em}}12\text{\hspace{0.17em}\hspace{0.17em}mins}$

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