Question

2 by 11 of the number of Shoulders in a regiment died of illness 2/15 of the number where killed in war and the remaining 22600 soldiers fled away what was the number of soldiers in a regiment

Answer 1

Given:-

• 2/11 soldier died by illness.

• 2/15 soldier killed in war.

• Remaining soldiers are 22600 ,they fled away .

To Find :-

• Total number of soldiers .

Solution :-

Let's assume that the total number of soldiers were x.

→ Total soldiers = soldiers killed by illness + soldiers killed in war + soldiers fled away.

→ Soldiers killed by illness = (2/11)x

→ Soldiers killed by war = (2/15)X

→ Soldiers fled away = 22600

But we we are not provided with the fraction value of soldiers fled away. So, let them as y .

→ 2/11 + 2/15 + y = 1

$\sf{ \implies \: \frac{2(15) + 2(11) + y(11 \times 15)}{11 \times 15} = 1 }$

$\sf{ \implies \: \frac{30 + 22 + 165y}{165} = 1 }$

$\sf{ \implies \: 52 + 165y = 165}$

$\sf{ \implies \: 165y = 165 - 52}$

$\sf{ \implies \: 165y = 113}$

$\sf{ \implies \: y = \frac{113}{165}x = 22600 }$

→ 113x = 22600 × 165

→ 113 X = 3729000

→ X = 3629000/113

→ X = 33000 .

So the total number of soldiers was 33000.

→ Soldiers died by illness = 2×33000/11

→. 6000

→ Soldiers died in war = 2 × 33000/15

→ 4,400

Answer 2

Answer:

☢ Given : 2/11 of the number of soldiers in a regiment died of illness. 2/15 of the number where killed in war and the remaining 22600 soldiers fled away.

⠀

Let the Number of Soldiers be n

⠀⠀⠀$\rule{160}{1}$

☯ $\underline{\boldsymbol{According\: to \:the\: Question :}}$

$:\implies\sf Total=Illness+Killed+Fled\:Away\\\\\\:\implies\sf n=\left(n \times \dfrac{2}{11}\right)+\left(n \times \dfrac{2}{15}\right)+22600\\\\\\:\implies\sf n = \dfrac{2n}{11} + \dfrac{2n}{15} +22600\\\\\\:\implies\sf n = \dfrac{(15 \times 2n) + (11 \times 2n)}{11 \times 15} + 22600 \\\\\\:\implies\sf n = \dfrac{30n + 22n}{165} + 22600\\\\\\:\implies\sf n = \dfrac{52n}{165} + 22600\\\\\\:\implies\sf n - \dfrac{52n}{165} = 22600\\\\\\:\implies\sf \dfrac{165n - 52n}{165} = 22600\\\\\\:\implies\sf \dfrac{113n}{165} = 22600\\\\\\:\implies\sf n =22600 \times \dfrac{165}{113} \\\\\\:\implies\sf n = 200 \times 165\\\\\\:\implies\underline{\boxed{\textsf{n = 33,000}}}$

⠀

$\therefore\:\underline{\textsf{Number of soldiers in regiment was \textbf{33,000}}}.$