Question

in a 13 round tv match, two boxer a and b compete for gold medal. the boxer a delivers 8 punches in the first round and his punch delivery increases by 1 in each successive round. the boxer b delivers 4 punches in the first round and his punch delivery increases by 2 punch in each successive round. of 1 punch delivered equals 1 point, then who should win the gold medal

Answer 1

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This is a question of arithmetic progression.

n = 13

We need to find whose sum of terms of AP is greater.

For boxer A,
a = 8
d = 1

S = ½×n[2a+(n-1)d]
= ½×13(16+12×1)
= ½×13×28
= 182

For boxer B
a = 4
d = 2

S = ½×13(8+12×2)
= ½×13×32
= 208

Since number of punches of B are greater than those of A, B will have more points.
Thus, B will get the medal.

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Answer 2

Given : Total Number of Rounds = 13

Let us Calculate Total Number of Punches delivered by Boxer A in 13 Rounds

Given that Boxer A delivers 8 Punches in the 1st Round and his Punch Delivery increase by 1 in each Successive round.

⇒ 1st Round Punches of A = 8

⇒ 2nd Round Punches of A = 9

⇒ 3rd Round Punches of A = 10

We can notice that the Punches of A are in Arithmetic Progression with 1st Term (a) = 8 , Common Difference (d) = 1 and n = 13

We know that Sum of 'n' terms is Given by :

$S_n = \frac{n}{2}({2a + (n - 1)d)$

Total Number of Punches of A = $\frac{13}{2}(2(8) + (13 - 1)1)$

⇒ $\frac{13}{2}(16 + 12) = \frac{13}{2}(28) = 13\times14 = 182$

Number of Points of A = 182

Let us Calculate Total Number of Punches delivered by Boxer B in 13 Rounds

Given that Boxer B delivers 4 Punches in the 1st Round and his Punch Delivery increase by 2 in each Successive round.

⇒ 1st Round Punches of B = 4

⇒ 2nd Round Punches of B = 6

⇒ 3rd Round Punches of B = 8

We can notice that the Punches of B are in Arithmetic Progression with 1st Term (a) = 4 , Common Difference (d) = 2 and n = 13

Total Number of Punches of B = $\frac{13}{2}(2(4) + (13 - 1)2)$

⇒ $\frac{13}{2}(8 + 24) = \frac{13}{2}(32) = 13\times16 = 208$

Number of Points of B = 208

As, Points of B are Greater than A :

⇒ B is the Winner of the Gold Medal