Question

49. 1200 soldiers in a fort had enough food for 28 days. After 4 days, some soldiers were transferred to another fort and thus the food lasted now for 32 more days. How many soldiers left the fort?

a. 300

b. 400

c. 200

d. 100




50. If the perimeter of an isosceles right is (6 + 3√2) m, then the area of the triangle is triangle is:

a. 5.4m²

b. 81 m²

c. 9m²

d. 4.5m²








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Answer 1

Step-by-step explanation:

The number of soldiers who were sent to another fort lasted for 4 days in this fort.

So the number of days left for enough food = (28 – 4) = 24 days.

So 1200 soldiers had enough food for 24 days after the 4 days.

Therefore 1200 soldiers = 24 days.

Now when (x) soldiers sent to another fort after 4 days the food left for another 32 days

Therefore (1200 – x) soldiers = 32 days.

So as we see that when the number of soldiers decreases, the food would last for more days thus there is an inverse variation between soldiers and number of days.

Therefore we get,

⇒1200×24=(1200−x)32⇒1200×24=(1200−x)32

 Now simplify the above equation we get,

⇒1200×24=1200×32−32x⇒1200×24=1200×32−32x

⇒32x=1200(32−24)=1200(8)⇒32x=1200(32−24)=1200(8)

⇒x=1200×832=12004=300⇒x=1200×832=12004=300.

Therefore 300 soldiers left the fort after 4 days.

So this is the required ans

Ans 2nd

In an isosceles right angled triangle, the two sides on the right angle are equal.

Let the equal sides be a.

Hence, hypotenuse of the isosceles right angled triangle =a2+a2=2a

Given, perimeter of the triangle =(6+32)m

⇒a+a+2a=(6+32)m

⇒a(2+2)=3(2+2)m

⇒a=3m

In the isosceles right triangle, the base and height =a

Hence, area of the triangle =21×base×height =21×3×3=4.5m

Answer 2

Answer:

Question :-

49. 1200 soldiers in a fort had enough food for 28 days. After 4 days, some soldiers were transferred to another fort and thus the food lasted now for 32 more days. How many soldiers left the fort?

a. 300

b. 400

c. 200

d. 100

♣ $\tt \pink{\underline{Required \: Answer}}$

$\tt{\underline{\underline{correct \: option \: is \:A ♐}}}$

Total amount of food available initially:  1200 ×28    Soldier-days

After 4 days, the amount of food remaining:  1, 200 × 24  soldier-days worth.

Let N soldiers be remaining after some are transferred to another fort.

     1, 200 × 24  = N × 32

               N = 900

  Hence,  300 soldiers were transferred.

============================

Proportional method

     As the number of soldiers decreases, the number of days the food lasts will increases.  As the number of soldiers increases, the number of days the food lasts, will decrease.  So number N  of soldiers is inversely proportional to the number D of days.

               So    N = K / D,    where  K = constant of proportionality

                     when  N = 1,200  then  D = 24

             So  K = N D = 1,200 × 24

  

       When D = 32,  N = K / D = 1, 200 × 24 / 32 = 900

•      Hence, there were only 900 soldier after 4 days.    So 1200 - 900 = 300 soldiers are transferred.

__________________________

Question :-

50. If the perimeter of an isosceles right is (6 + 3√2) m, then the area of the triangle is triangle is:

a. 5.4m²

b. 81 m²

c. 9m²

d. 4.5m²

♣ $\tt \pink{\underline{Required \: Answer}}$

$\tt{\underline{\underline{correct \: option \: is \: D ♐}}}$

$\huge \mathcal \red{Let}$

a = the length of the equal sides, then hypotenuse is:

c² = a² + a²

c = a√2

P = a + a + a√2 = 6 + 3√2

2a + a√2 = 6 + 3√2

a = 3 units

A = 1/2 × 3 × 3

A = 9/2 = 4.5²

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