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Question

Sachin, Sehwag and Dhoni together scored 228 runs. Their individual scores are in G.P. Sehwag and Dhoni together scored 12 runs more than Sachin. Find their individual scores.

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Solution

Let the runs made by Sachin, Sehwag and Dhoni be ar, a and ar, respectively.
Thus, we have:
ar + a + ar = 228 …(1)
Sehwag and Dhoni together scored 12 runs more than Sachin.

Thus, we have:
a + ar = ar + 12
a + ar – ar = 12 …(2)
On subtracting (2) from (1), we get:
ar+ a + ar – a – ar + ar = 228 – 12 = 216
2ar = 216
a = 108r
On putting a = 108r in (1), we get:

108rr+108r +108r2 = 2281081+r+r2 =2281+r+r2 = 199r+r2 =109

On using the quadratic formula, we get:

r=-1±1-4×1×-1092(1) =-1±1+4092 =-1±4992 =-1±732 =-3±76 =-106and 46 = -53and 23

For r = -53, we have:
a = 108 × -53 = -180 < 0
The value cannot be negative.

For r =23, we have:
a = 108 × 23 = 72

Thus, we have:

ar=7223=72×32=108a=72ar=72×23=48

Therefore, Sachin scored 108 runs, Sehwag scored 72 runs and Dhoni scored 48 runs.

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