time taken for their 1st meeting (Question:586501.0)

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Arnab Deb

· started a discussion

· 1 Months ago

time taken for their 1st meeting (Question:586501.0)

time taken for their 1st meeting is becoming 13.67

Question:

Aman and Suman are running on a circular track of radius 250 m. Aman takes 40 sec to complete a round and speed of Suman is half of Aman. They started simultaneously towards each other from diametrically opposite points on the circular path. If they first meet at a point A, then after how much time from the start do they meet at point A for fifth time?

Options:

5 Minutes $26 \frac{23}{42}$ S

7 Minutes $21$ S

4 Minutes $18$ S

6 Minutes $26 \frac{23}{42}$ S

Solution:

Ans: (a)

Length of track = 2 × $\frac{22}{7}$ × 250

= $\frac{11000}{7}$ m.

Time taken by Aman = 40S.

Time taken by Suman = 80 Sec (∵ Speed is half)

Distance to be covered for first meeting = $\frac{5500}{7}$ m.

Speed of Aman =

Speed of Suman =

Time taken for first meeting = $\frac{5500}{\frac{7}{80 + 40}}$

= $\frac{5500}{7 \times 120} = \frac{275}{42}$

= $6 \frac{23}{42}$ Sec.

Time taken for next time meeting at the same point = L.C.M. of time taken

= L.C.M. of (80, 40) = 80

∴ Time taken in 5^th meeting =

$6 \frac{23}{42} + 4 \times 80$

= $6 \frac{23}{42} + 320$

= 326 $\frac{23}{42}$ S.

= 5 Minutes $26 \frac{23}{42}$ S

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