Question

Three boys A,B,C start running at constant speeds from the same point P along the circumference of a circular track. Speeds of A,B,C are in the ratio 5:1:1. A and B runs clockwise while C runs anticlockwise. Each time A meets B or C on the track, he gives them a card. What is the difference in the number of cards received by B and C if A distributes 33 CARDS in total​

Answer 1

Answer:

A: B : C = 5:1:1 ===> A & B meet at 4 distinct points ;

A & C will meet at 6 distinct points.

When a complete 5 round b& c will complete 1 round

=> a meets b 4 times & a meets c 6 times ( one cycle is completed).

So at the end of 3 cycle A meets B 12 times & with C 18 times.

Now in his 16th round A will meet with C but not with B ( as a& b are travelling in same direction so a will be ahead of b) and in his 17th round he meet B & C once.

So for b = 12+1 = 13 & for c = 18+2 = 20 ;

So difference = 20-13=7.

so answer is 7

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Answer 2

Given :- Three boys A,B,C start running at constant speeds from the same point P along the circumference of a circular track. Speeds of A,B,C are in the ratio 5:1:1. A and B runs clockwise while C runs anticlockwise. Each time A meets B or C on the track, he gives them a card. What is the difference in the number of cards received by B and C if A distributes 33 cards in total ?

Solution :-

→ Speed of A : B : C = 5 : 1 : 1

so,

→ Speed of A / Speed of B = 5 / 1

→ Speed of A / Speed of C = 5 / 1

now, we know that,

• In Opposite direction = If the speed of A is x/y of B, then the total number of meeting points = x + y.
• In same direction = If the speed of A is x/y of Y, then the total number of meeting points = x - y .

since speed of A is 5 times of B and C ,

→ A and B meets = 4 times (same direction)

→ A and C meets = 6 times (opposite direction)

then,

→ Total times they meets = 6 + 4 = 10 times .

Multiply by 3 we get in 30 times ,

→ A and B meets = 4 * 3 = 12 times

→ A and C meets = 6 * 3 = 18 times .

now, for next 3 meeting , Since A and B are in same direction A will meet him only 1 time and meets C 2 times .

therefore,

→ Total cards B have = 12 + 1 = 13 cards

→ Total cards C have = 18 + 2 = 20 cards

hence,

→ Difference between cards recieved = 20 - 13 = 7 cards (Ans.)

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