Question

A Garrison had sufficient food for 460 soldiers for 40 days. After 10 days 140 more soldiers came to the fort. How many days will the provisions last at the same rate
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Answer 1

Given :

460 soldiers = 40 days.

After 10 days, = 140 soldiers joined.

According to the question :

After 10 days :

=> Total days - 10

=> 40 - 10

=> 30 days.

For 1 soldier, provisions are sufficient for,

=> 30 days × 460 soldiers

Total soldiers :

=> 460 + 140 joined

=> 600 soldiers.

Equation :

☞ 30 days × 460 soldiers / Total soldiers

=> 30 × 460 / 600

=> 138 / 6

=> $\sf\large\underline\blue{23 days}$.

Answer 2

${ \bf{ \underline{ \red{ \underline{ \red{Question }}}} : - }}$A Garrison had sufficient food for 460 soldiers for 40 days. After 10 days 140 more soldiers came to the fort. How many days will the provisions last at the same rate.

${ \bf{ \underline{ \red{ \underline{ \red{ Given}}}} : - }}$

• a ) A Garrison had sufficient food for 460 soldiers for 40 days.
• b ) After 10 days 140 more soldiers came to the fort

${ \bf{ \underline{ \red{ \underline{ \red{ Find}}}} : - }}$

• How many days will the provisions last at the same rate.

${ \bf{ \underline{ \red{ \underline{ \red{ Solution}}}} : - }}</p><p>$

Now, { from given } [After 10 days 140 more soldiers came to the fort]

Hence, we substract 10 day's from 40 day's.

=>40day's - 10day's = 30day's ...( 1 )

we know that soldier's are increased after 10 day's Hence,

=> 460 soldier's + 140 soldier's

= 600 soldier's ... ( 2 )

According to eq. ( 1 )

=> 460 soldier's = 30 days .... ( 3 )

According to eq. ( 2 ) Let, day's be x

=> 600 soldier's = x day's .... ( 4 )

Now, to find days for the provisions

last at the same rate.

we use an inverse proportion

{ from ( 3 ) & ( 4 ) }

=> 460 : 600 : : 30 : x

=> x = ( 460 × 30 )/600

=> x = 13800/600

=> x = 23 day's

Hence, the provisions will last for

23 day's at the same rate.

i hope it helps you.