Question

A camp had provisions for 490 soldiers for 65 days. After 15 days, more soldiers arrived and the remaining provisions lasted for 35 days. How many soldiers joined the camp??

Answer 1

The number of additional soldiers who joined the camp = 210

Provision for 490 soldiers is for 65 days at the camp.

After 15 days -

The provision for 490 soldiers will last for 50 days .

Let the number of soldiers arriving at the camp after 15 days be x.

Total soldiers at the camp = (490+x)

Number of days the provision lasted after new soldiers joined the camp = 35.

For 490 soldiers provision will last for 50 days .

For (490+x) soldiers provision will last for 35 days .

So, 490 × 50 = (490+x) × 35

=> 7350 = 35x

=> x = 210

210 additional soldiers joined the camp.

Answer 2

Answer:

★ Number of soldiers joined the camp was 210 ★

Step-by-step explanation:

Given: Let camp has provision of food

• Provision of food for 490 soldiers is for 65 days
• After 15 days, more soldiers arrived and the remaining provisions lasted for 35 days

To Find:

• Number of soldiers who joined camp

Solution:

† In first case †

Total number of soldiers = 490 and Number of days = 65 days

† In second case † ( After 15 days)

Total number of soldiers= 490 and Number of days = 65–15 = 50 days

★ After 15 days some more soldiers arrived the camp. ★

→ Let number of soldiers joined the camp be x

∴ Number of soldiers = 490 + x and Number of days = 50–15 = 35 days

A/q

Soldiers 490 then Days = 50

Soldiers 490 + x then Days = 35

Here, As the number of soldiers increased then the number of days decreased. Therefore, It is in Inverse Proportion

→ Proportion is (490+x) : 490 : 50 : 30

★ Product of Extremes = Product of Means

$\small\implies{\sf }$ (490+x)35 = 490 x 50

$\small\implies{\sf }$ 17,150 + 35x = 24,500

$\small\implies{\sf }$ 35x = 24,500–17,150

$\small\implies{\sf }$ 35x = 7350

$\small\implies{\sf }$ x = $\large{\sf {\frac{</strong><strong>7</strong><strong>3</strong><strong>5</strong><strong>0</strong><strong>}{</strong><strong>3</strong><strong>5</strong><strong>}}}$ = 210

Hence, The number of soldiers who joined the camp was 210