28 hrs

Son in law

3.1

Perimeter of semi circular = πr+2r

Where r is radius , π = 22/7

πr+2r= 144 (given)

(22/7)r +2r = 144

22r+14r = 144*7 (multiply both sides by 7)

36r = 144*7

r= 144*7/36 = 28

radius =28 cm

Area =( 1/2)πr^2

Area=( 1/2 )*(22/7)*28*28

= 1232cm^2
Ans : area is 1232 cm^2

10

20

Explanation:

The number of ways of selecting three men, two women and three children is:

= ⁴C₃ * ⁶C₂ * ⁵C₃
= (4 * 3 * 2)/(3 * 2 * 1) * (6 * 5)/(2 * 1) * (5 * 4 * 3)/(3 * 2 * 1)
= 4 * 15 * 10
= 600 ways.

360

1.7% loss

1:2:3 or 1:2:4

speed = distence / time
60km/hr=distance / 9 sec
km / hr to m / s==> 60*1000 / 1* 3600 = 16.667
16.667*9 = distance
150 m is the answer

Answer is 400.(14^2=196, 16^2=256, 18^2=324, 20^2=400.)

Question does not clarify if its simple interest or compound interest

12 month=>900Rs+Uniform
1month:75 => 9month:675
675-650=25 =>price of Uniform

Sum of all numbers in series= 870 (I.e 312+162+132+142+122)
Average=sum of numbers/count of numbers
Average= 870/5
= 174

Answer: 40

Explanation:
800*(25/100) = 200 —- 5

? —- 1 => Rs.40

900

Out of 10 persons, 4 are graduates; so, (10 – 4) = 6 are under-graduates.

If there is no restriction, any three can be chosen from the ten in (10C3) = 120 ways.

Now, if all three chosen are under-graduates; it can take place in (6C3) = 20 ways.

Therefore, the probability that there will be no graduate among the three chosen = (20 / 120) = (1 / 6).

Therefore, the probability that there will be at least one graduate among the three chosen = {1 – (1 / 6)} = (5 / 6) = 0.8333.

30mins

Let the total time taken to fill the tank be x minutes.

Then, work done by B in half hour + work done by (A+B) in half hour =1.

(
40
1
​
×
2
x
​
)+(
60
1
​
+
40
1
​
)×
2
x
​
=1

⇒
80
x
​
+
48
x
​
=1

⇒
240
3x+5x
​
=1

⇒8x=240

⇒x=30 min