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.

• A. 108, 72, 48
• B. 108, 82, 48
• C. 84, 72, 48
• D. 108, 72, 44

Answer 1

The correct option is A 108, 72, 48

Let runs scored by Sachin, Sehwag and Dhoni be $\frac{a}{r},aandar$ respectively.
As per the given,
$\frac{a}{r}+a+ar=228⟹a+ar+a{r}^2=228r$
Also, $\frac{a}{r}+12=a+ar⟹a+12r=ar+a{r}^2$
From the above equation, substituting for $ar+a{r}^{2}asa+12r$, we get
$a+a+12r=228r⟹2a+12r=228r⟹a=108ror\frac{a}{r}=108$
So, Sachin scored 108 runs.
Substituting for a as 108r, we get
$a+ar=\frac{a}{r}+12⟹108r+108r^2=120⟹9r+9r^2=10$
Factorising, we get 'r' = 2/3 , -5/3
Since runs cannot be in negative, we will consider 'r' to be 2/3.
So, a = 108r or a = 72.
Sehwag scores 72 runs and Dhoni scores 48 runs.