Explanation

21 binders bind 1400 books in 15 days, so 1 binder binds:

1400/21 = 66.67 books in 15 days

= 66.67/15 = 4.44 books per day

To bind 800 books in 20 days, we need:

800/20 = 40 books per day

Number of binders required = 40/4.44 = 9

So, 9 binders are required to bind 800 books in 20 days.

Explanation

In the figure, MN is the length of the ladder, which is placed against the wall AB and makes an angle of ${60}^{\circ }$ with the ground.
The foot of the ladder is at N, which is 2m away from the wall.
$\therefore BN=2m$
In right-angled triangle MNB :
$cos{60}^{\circ }=\frac{BN}{MN}=\frac{2m}{MN}$
$\Rightarrow \frac{1}{2}=\frac{2m}{MN}$
$\Rightarrow MN=4m$
Therefore, the length of the ladder is 4m.

Explanation

(2.39)^2 - (1.61)^2 = 3.1400

2.39 - 1.61 = 0.78

3.1400 ÷ 0.78 = 4.0256 ≈ 4

Explanation

0.232323....=0.23

Let x=0.23                 ---- ( 1 )

Multiplying both sides by 100 we get,

⇒  100x=23.23         ---- ( 2 )

Subtracting ( 1 ) from ( 2 ) we get,

⇒  100x−x=23.23−0.23

⇒  99x=23

∴  x=9923​

∴   Required fraction is 9923​.

Explanation

Initial situation: 200 men have enough food for 60 days.

Reduced situation: 160 men (40 fewer men than initially).

Since there are fewer men, the food will last longer. To find out how long, we can set up a proportion:

200 men / 160 men = 60 days / x days

Where x is the number of days the food will last with 160 men.

Cross-multiplying and solving for x:

200x = 60 × 160

200x = 9600

x = 9600 ÷ 200

x = 75

So, the food will last 75 days if the number of men in the camp is reduced to 160.

Explanation

12 men=15women

1man=(15/12)=(5/4) women

7 men=35/4 women

(35/4+5 )=55/4

15 women=14 days

55/4 women=(15*14*4)/55= 168/11 days

Explanation

P1 = Rs.800

P2 = Rs.400

Time = 2 years

Difference in S.I. = Rs.40

Formula used:

S.I. = (PRT)/100

Calculation:

(P1RT)/100 – (P2RT)/100 = 40

⇒ RT(800 – 400) = 4000

⇒ R = 4000/800

⇒ R = 5%

∴ The rate of simple interest is 5%.

Explanation

log5​512=log5log512​
=log(10/2)log29​
=log10−log29log2​
=1−0.30109×0.3010​
=0.6992.709​
=6992709​
=3.876

Explanation

C for each week
S students
how many weeks will X last?
let the number of weeks be W.
for each week, there will be X/W cans of soup.

Each student will take C cans of soup
So S students will take SC cans
we know X/W = SC
W= X/SC

Explanation

x = 3+ √8

x = (3+√8)(3-√8) / (3-√8)

x = (9 -8) / (3-√8)

x = 1/ (3 -√8)

Or we can write 1/x = (3-√8)

Put the value and find out

x² +(1/x²) = x² + (1/x)²

So x² + 1/ x² = (3 +√8)² + (3 -√8)²

= 9+6√8+8 + 9–6√8+8

= 34.