Question

Four persons P, Q , R and S start running around a circular track simultaneously.If they complete one round in 10,8,12 and 18 minutes respectively,after how much time will they next meet at the starting point
a)180 min b) 270min c)360min d)450 min 4)

Answer 1

Step-by-step explanation:

The inside perimeter of the track =400m

The total length of the two straight portions =90+90=180m

Therefore the length of the remaining portion =400−180=220m

Circumference of the two remaining semi-circular portions =πr+πr=2πr. ′r′ is radius

⇒  2πr=220

⇒  2×722×r=220

∴  r=35m

So, the radius of the circular portion of the outer running running track =35m+14m=49m

Area of the track = Area of the two rectangles of dimensions  + The area of the circular rings.

⇒  Area of track =2×90×14+722×[(49)2−(35)2]

⇒  Area of track =2520+722×(2401−1225)

⇒  Area of track =2520+722×1176

⇒  Area of track =2520+3696

∴  Area of track =6216m2

⇒  Length of the outer running track =2×90+2×722×49

Answer 2

Given: Four persons P, Q , R and S start running around a circular track simultaneously. They complete one round in 10,8,12 and 18 minutes respectively.

To find: Time after which they will meet next at the starting point

Solution: Time taken by P= 10 minutes

Time taken by Q= 8 minutes

Time taken by R= 12 minutes

Time taken by S= 18 minutes

For finding the time after which they meet together, we need to find the lowest common multiple(LCM) of the given numbers.

For finding LCM by prime factorisation method,

Prime factorisation of 10 =

${2}^{1} \times {5}^{1}$

Prime factorisation of 8=

${2}^{3}$

Prime factorisation of 12=

${2}^{2} \times {3}^{1}$

Prime factorisation of 18=

${3}^{2} \times {2}^{1}$

The LCM will be the product of the greatest power of each prime factor given in the numbers.

Therefore, LCM=

${5}^{1} \times {2}^{3} \times {3}^{2}$

= 360

Therefore, they will meet together at the starting point after option (c) 360 minutes.