21. In a square, all the mid points are
joined. The inner square is shaded. If the area of the square is A, what is the
area of the shaded area?

Ans. the shaded area is half the area of the
square (having area A). Therefore
answer is A/2.

22. If a team consists 20 members in which 20% are mathematician then how many member should they hire sothat the ratio would become 10/11.

Ans. 20*20/100=4,so there are 4mathematician,'x' be the number of members added together,so x+4/x+20=10/11.therefore x=156.

Ans. 20*20/100=4,so there are 4mathematician,'x' be the number of members added together,so x+4/x+20=10/11.therefore x=156.

23. You have two jars, 50 red marbles and 50
blue marbles. A jar will be picked at random, and then a marble will be picked
from the jar. Placing all of the marbles in the jars, how can you maximize the
chances of a red marble being picked? What
are the exact odds of getting a red marble using your scheme?

24. Using the numerals 1,7,7,7 and 7 (a
"1" and four "7"s) create the number 100. As
well as the five numerals you can use the usual mathematical operations +, -,
x,/ and brackets ().

Ans.
(7+7) × [7+(1 / 7)] = 100

25. A girl, a boy, and a dog start walking
down a road. They
start at the same time, from the same point, in the same direction. The
boy walks at 5 km/h, the girl at 6 km/h. The
dog runs from boy to girl and back again with a constant speed of 10 km/h. The
dog does not slow down on the turn. How
far does the dog travel in 1 hour?

Ans.
10km. Because the dog's speed is 10 km/h.

Where
the boy and girl are has no effect on answering this puzzle.

26. There are 2 trees in a garden (tree
"A" and "B") and on the both trees are some birds.

The
birds of tree A say to the birds of tree B that if one of you come to our tree,
then our population will be the double of yours. Then
the birds of tree B tell to the birds of tree A that if one of you come here,
then our population will be equal to that of yours. How
many birds in each tree?

Ans. Let the birds on Tree A = x

Birds
on Tree B = y

According
to question :

When
1 bird fly from tree B to tree A

Trees
of A = x + 1

Trees
on B = y - 1

x
+ 1 = y - 1

=>
y-x = 2........(i)

When
1 bird fly from tree a to tree b

Birds
on Tree A = x - 1

Birds
on Tree B = y +1

y
+ 1 = 2 ( x - 1 )

2x-y
= 3............(ii)

From
equation (i) and (ii), we get

x=
5 and y = 7.

27. There are two bags, one of which contains 5 red and 7 white balls and the other 3 red and 12 white balls. A ball is to be drawn from one or other of the two bags ; find the chances of drawing a red ball.

Ans. 37/120

28. Karthik started a business investing Rs.9000. After 5 months, Shyam joined with a capital of Rs.8000. If at the end of the year, they earn a profit of Rs.6970, then what will be the share of Shyam in the profit?

Ans. 2380

29. A Black Smith was given a chain torn into equal sections of 3 links each and asked to fix it. How many links(minimum) would he has to open up and reforge ?

Ans. To join 2pieces of 3links one link must be open and to join next two pieces one more link needs to be opened. so, total no. of links which needs to be opened is 2.

30. A square plate of some size is cut at four corners. Equal squares of the same size are cut and is formed as open box. If this open box carries 128 ml of oil. What is the size of the side of the plate?

###
(a) 17

27. There are two bags, one of which contains 5 red and 7 white balls and the other 3 red and 12 white balls. A ball is to be drawn from one or other of the two bags ; find the chances of drawing a red ball.

Ans. 37/120

28. Karthik started a business investing Rs.9000. After 5 months, Shyam joined with a capital of Rs.8000. If at the end of the year, they earn a profit of Rs.6970, then what will be the share of Shyam in the profit?

Ans. 2380

29. A Black Smith was given a chain torn into equal sections of 3 links each and asked to fix it. How many links(minimum) would he has to open up and reforge ?

Ans. To join 2pieces of 3links one link must be open and to join next two pieces one more link needs to be opened. so, total no. of links which needs to be opened is 2.

30. A square plate of some size is cut at four corners. Equal squares of the same size are cut and is formed as open box. If this open box carries 128 ml of oil. What is the size of the side of the plate?

###
(a) 17

(b) 14

(c) 13

(d) None of these

Ans. Let, side of original plate be =x

Also, side of the square at the corners= a

so, when the square at the corner is cut off, the length of the box is=x-2a

similarly, the breadth of the box is=x-2a

the height of the box would be invariably=a

so, the dimension of the open box=(x-2a)*(x-2a)*a=a*(x-2a)^2

so, we need to factorize 128 so that we get a square term & an integer.

case 1. 128=2*2*2*2*2*2*2=(2*2*2*2*2)*2*2=32*2*2

so, a=32, x-2a=2, x=2*32+2=66

case 2. 128=2*2*2*2*2*2*2=(2*2*2)*(2*2)*(2*2)=8*4*4

so, a=8, x-2a=4, x=2*8+4=20

case 3. 128=2*2*2*2*2*2*2=2*(2*2*2)*(2*2*2)=2*8*8

so, a=2, x-2a=8, x=2*2+8=12

so, the possible values of the side of the original square plate are 66, 20 & 12

none of these match the answer options provided in a. , b. or c.

so, the correct choice is (d) None of these.

Good Collection!

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