3. Two goats are tied with a rope of length 40m outside of a rectangular shed of dimensions 50m X 30m. The goats are tied to different corners which lie on the opposite ends of a diagonal of the shed. What is the area in which the two goats can eat grass, if they choose not to eat in the common approachable area?
Given rope of length = 40m (radius)
Area of semi circle =(pi*r^2)/2 = (1600 * pi)/2 = 800*pi ---(1)
Area of quarter circle = (1/2 * 800 * pi) = 400*pi ----- (2)
Area of sector is = r*r*(pi/2)/2 = 25*pi ----- (3)
By adding above eq. (1) (2) & (3)
Total area = 1225*pi
As per quesiton there are 2 goats
so area = 1225*pi*2 = 2450pi
4. In a society of 80 resident families who subscribe newspapers, 60% of them subscribe The Hindu newspaper, 80% of them subscribe regional language newspaper and 70% of them subscribe TOI. How many families could, at the least, be subscribing to all the three newspapers
Total no. of families who take newspaper=80
Hindu newspaper = 60% = (80*60/100) = 48
Regional newspaper = 80% = (80*80/100) = 64
TOI newspaper = 70% = (70*80/100) = 56
Find common families take H.C.F (48,64,56) = 8
So, common families who take all newspaper = 10%.
8. A person travels in a car with uniform speed. He observes the milestone,which has 2 digits. After one hour he observes another milestone with same digits reversed. After another hour he observes another milestone with same 2 digits separated by 0. Find the speed of the car?
First milestone : 10x+y
Second milestone : 10y+x
Third milestone: 100x+y
Since the speed is uniform so
Distance covered in first Hr = Distance covered in Second Hr
(10y+x)-(10x+y) = (100x+y)-(10y+x)
but since x and y are digits so only possible combination is x=1 and y=6,
So average speed = 45 Kmph
10. There are 8 people, F, G, H, J, K, L, M, and N. 2 groups are to be formed. F will always go with J. G and M will never go together. H will always go with L. N will always go with G. What are the two groups to be formed?
8 people namely F,G,H,J,K,L,M,and N respectively.
Now we have to form 2 groups
1st condition: F will always go with J
Meaning: F and J always lie in same group. ............(i)
2nd condition:G and M will never go together.
Meaning: G and M always lie in different groups. .........(ii)
3rd condition:H will always go with L.
Meaning:H and L always lie in same group. .............(iii)
4th condition:N will always go with G.
Meaning:N and G always lie in same group. ..........(iv)
According to (i),(ii),(iii),and (iv)
2 groups can be formed in following 2 ways
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