some aptitude ques with ans

1) I have 20 rupees. I bought 1, 2, 5 rupee stamps. They are different in numbers by the reason of no change, the shop keeper gives 3 one rupee stamps. So how many stamp(s) I have.
Ans: 10

Explanation:

(a) 3 x 1 rupee, 1 x 2 rupee, 3 x 5 rupee
(b) 3 x 1 rupee, 6 x 2 rupee, 1 x 5 rupee
(c) 4 x 1 rupee, 3 x 2 rupee, 2 x 5 rupee
and one can think of others e.g.
(d) 11 x 1 rupee, 2 x 2 rupee, 1 x 5 rupee
(e) 9 x 1 rupee, 3 x 2 rupee, 1 x 5 rupee

 the point is that the requirement that the shopkeeper gives 3 one-rupee stamps eliminates all solutions other than the first two.that in turn forces the solution to contain an odd number of 5 rupee stamps, as no amount of 2-rupee stamps can add up to an odd number of rupees.There is a solution with one 5-rupee stamp (b) and a solution with three 5-rupee stamps (a).

2) An Engine length 1000 m moving at 10 m/s. A bird is flying from engine to end with x kmph and coming back at 2x. Take total time of bird traveling as 187.5 s. Find x and 2x.

 Ans:8,16.

Explanation:

distance travelled by the bird=2000m
time taken=187 1/2 sec
=375/2 sec
speed is in the ratio of 1:2
dividing the time in the ratio of 1:2
time while moving to end=375/2(2/3)=125 sec
speed=distance/time=1000/125=8 m/sec
speed in the fro direction=16m/sec

3) All persons know either swimming or rowing.
There are 14 persons who know only swimming and 14 persons who know only rowing. 8 tickets sold for rowing. How many people are there for swimming?

Explanation:

we need atleast one of the values i.e either total no. pf membrs or no.of mem who know both to find the otherwhere n(a U b) = n(a - b) + n(b-a)+n(a intersection b)
Given,8 tickets sold for rowing..from this we can deduce that 6 people who know only rowing did not buy tickets.but we have no idea how many people know both..Even if we knew this, not everyone needs to buy a ticketSo, question is totally incomplete

4) Which polygon has no. of sides = diagonal

 Ans:Pentagon

Exp:

the number of diagonals from a single vertex is three less than the the number of vertices or sides, or (n-3).

There are N vertices, which gives us n(n-3) diagonals

But each diagonal has two ends, so this would count each one twice. So as a final step we divide by 2, for the final formula:

where N  is the number of sides (or vertices)

5) One Cigar can be made from 7 bits. If there are 16 Cigars then how many bits collected?
Ans: 4

Exp:

The question is assuming that the bit is what is left after smoking..........

 So 16 cigars are smoked so you have 16 bits left. You take 14 bits to make 2 cigars and have 2 bits left over.

 you smoke the final 2 cigars and now you have the two bits from them plus the other two left over bits for a total of 4......:)

6) A, B, C, D went to a hotel and planned to share the bill equally. But afterwards they changed their plan and to pay proportional to consumption A paid 240, B & C paid equally, D paid only half the amount that he should have paid based on the first plan. What is the amount paid by B?

Ans:Rs.160

Exp:

B = C
A = 240
D = 25%/2
It should have been 25% for each, but they paid proportionally.
So if D paid 12.5% of the bill, then that leaves 87.5% of the bill for the other 3.
If B and C paid the same, then A had to take over the other 12.5% of D's bill based on consumption.

25% + 12.5% = 37.5% = % paid by A

37.5% + 12.5% = 50%

100-50 = 50%

Since B and C paid the same, B paid 25% of the bill.
Since we know that 240 rupees is 37.5% of the bill, use a proportion to find the amount of the whole bill.

240/.375 = x/1
x = Rs.640

Do the percentages based on what we know:
A = Rs.240
B = Rs.160
C = Rs.160
D = Rs.80

B paid Rs.160

Lone rider, you don't need the final bill amount to figure out how much B paid.

You only need to know that there are 4 of them. They originally agreed to pay 25% of the bill each.

If D only paid half of the original 25%, then he only paid 12.5%.
If B and C paid the same, either they split the 12.5% in 6.75% each, or A took the 12.5% and tacked it onto his bill, which seems more likely.

7) There is a point P on the circle. A and B started running in two constant different speeds. A in Clockwise and B in Anti-clockwise. First time 500 m in Clockwise from P then 400 Anti-clockwise. If B is yet to complete one round, What is the circumference of the circle?

Ans:700m

Exp:

Let the speeds of A & B be u and v resp. and let circumference be C.Let their first meeting be after time t then ut+vt = C and ut = 500∴ vt = C−500 and u/v = 500/(C−500)For their second meeting after time T,                                                             uT+vT =2C and vT = 400

                        uT = 2C−400 and u/v = (2C−400 )/400

Hence 500/(C−500) = (2C−400) /400

.
Simplifying, 100000 = (C−200)(C−500) = C²−700C+100000 → C=700.....

8) There are 11 lines in plane.How many intersections (Maximum) can be made?

Ans:55

 Exp:

First line will cut all other 10, similarly second will cut 9, and so on
total = 10+9+8+7+6+5+4+3+2+1 = 55

9) There are 3 Sections with 5 Qns each.
If three Qns are selected from each section, the chance of getting different Qns is?

Ans:1000

Exp:

Methods for selecting 3 questions out of 5 in the first section = 5*4/2*1 = 10
similarly for others
so total methods = 10*10*10 = 1000

10) P # Q = (P-Q)(Q-P) = - 1. Then Which is true?
P = 3, Q = 2 P = 2,Q = 3 P = -1,Q = 1 P = 1, Q = -1
Ans: I & II only

11) 7 Pink, 5 Black, 11 Yellow balls are there. Minimum no. atleast to get one black and yellow ball
Ans: 17