1.A woman buys some shoe strips n then 4 times of that she buys packet pins n then 8 times of shoe strips she buys handkerchiefs...n she has a bill of Rs3.24...N she pays for each article as many paisa as there r articles (of that particular item).Now what’s the number of handkerchiefs?
Answer: 16
2.Let the no of shoe strips be x.then packet pins 4x.and handkerchiefs 8x.
Let a be the cost of a single shoe strip in paisa.
Let b be the cost of a single packet pins in paisa.
Let c be the cost of single handkerchiefs in paisa.
Answer: According to given second sentence. a = x; b =4x; c = 8x--- (1).
.but x.a+4x.b+8x.c=324--- (2).sub. 1 in 2 we get x^2 + 16x^2+64x^2 = 324.i.e.
81x^2 = 324; X= 2; the no of handkerchiefs = 8x=8(2) = 16.
3.One quarter of the time till now from midnight and half of the time remaining from now up to
Midnight adds to the present time. What is the present time?
Answer: 9:36AM
Let x be present time .therefore ¼(x-0) +1/2(24-x) = x. solving we get 9.6 which is 9 +.6 of an
Hour =9.36 am.
4.A man sold 2 pens. Initial cost of each pen was Rs. 12. If he sell it together one at 25% profit and
Another 20% loss. Find the amount of loss or gain, if he sells them separately.
Answer: 60 Paisa losses
CP1= [1/ (1+.25)]*12 = Rs 9.60
CP2= [1/] 1-.20)]*12 = Rs 15
Selling together -CP1+CP2 = Rs.24.60
Selling separately- 12+12 = Rs .24
Loss=60 paisa.
5.A boy asks his father, “what is the age of grand father?". Father replied " He is x years old in x^2 years", and also said, "we are talking about 20th century". What is the year of birth of grand father?
Answer: 1892
44*44=1936
Therefore 44 years old in 1936 so year of birth=1936-44=1892
6.A boy travels in a scooter after covering 2/3rd of the distance the wheel got punctured he covered the remaining distance by walk. Walking time is twice that of the time the boy’s riding time. How many times the riding speed as that of the walking speed?
Answer: 4 times.
X-total distance to be traveled
[2/3(x)]/a =T1 (a-ridding speed, T1-ridding time)
[1/3(x)]/b =T2 (b-walking speed T2- walking time)
T2=2T1
Equating we will get a=4b
7.In a Knockout tournament 51 teams are participated, every team thrown out of the tournament if they lost twice. How many matches to be held to choose the winner?
Ans: 101 matches
2n-1=2(51)-1=102-1=101
8. One-third of the persons in front of me together with 3/4th of the persons behind me equals the total number of the persons in the merry go round. Find the total number.
Answer:
(number in front = number behind = total number -1)
so,
(1/3)(n-1) + (3/4)(n-1) = n
n=13
9. A bus has a maximum speed of 100 km/h. With 3 people, the bus moves at a speed of 88 km/h. With 6 people what would be the velocity if the bus' speed decreases proportionately with the number of people in the bus.
Answer:
At 100 kmph, only driver is in the bus.
Persons speed
1 100
1+2 100 - 6*2 = 88 kmph
1+5 100 - 6*5 = 70 kmph
10. In an island, natives always lie and visitors always tell the truth. I met a salesman in a hotel in the island. I wanted to know whether the salesman was a native or a visitor. For that, instead of directly asking him, I asked him to ask a woman sitting in the nearby table whether she is a native or a visitor. The salesman asked the woman and said" she said she is a visitor". Is it possible to find whether the salesman was a visitor or a native? If so, what is he?
Answer:
The possible combinations for the salesman and the woman are
salesman woman
1. T T (Y)
2 F T (N)
3. T F (Y)
4. F F (N)
if 4,
then woman and salesman should have lied. so, the woman should
have said "i am a native", but she would be a visitor.(contradictory with
assumption that W-F)
if 3,
then woman had lied and salesman says the truth. So, the woman
should have said "i am a visitor", but she was a native. (Acceptable)
if 2,
then woman says the truth and salesman lied. So the woman should
have said "i am a native" , but she was a visitor.(contradictory with
assumption that W-T)
if 1,
then woman and salesman say the truth. so both are visitors.
(acceptable).
so, only 1 and 3 are acceptable (T, T) and (T,F). In both cases,
the salesman says the truth and is a visitor.
11. A 1 k.m. long wire is held by n poles. If one pole is removed, the length of the gap increases by 5/3 meters. What is the number of poles initially?
Answer:
if n poles,
(n-1) gaps of each 1000/(n-1) width
if n-1 poles,
(n-2) gaps of each 1000/(n-2) width
so,
1000/(n-2) - 1000/(n-1) = 5/3
1000(1/(n-2) -1/(n-1)) = 5/3
1000(1/((n-1)(n-2))) = 5/3
(n-1)(n-2) =(3/5) * 1000 = 600
as 600 = 25 * 24
n-1 = 25, n=26 poles
Answer: 16
2.Let the no of shoe strips be x.then packet pins 4x.and handkerchiefs 8x.
Let a be the cost of a single shoe strip in paisa.
Let b be the cost of a single packet pins in paisa.
Let c be the cost of single handkerchiefs in paisa.
Answer: According to given second sentence. a = x; b =4x; c = 8x--- (1).
.but x.a+4x.b+8x.c=324--- (2).sub. 1 in 2 we get x^2 + 16x^2+64x^2 = 324.i.e.
81x^2 = 324; X= 2; the no of handkerchiefs = 8x=8(2) = 16.
3.One quarter of the time till now from midnight and half of the time remaining from now up to
Midnight adds to the present time. What is the present time?
Answer: 9:36AM
Let x be present time .therefore ¼(x-0) +1/2(24-x) = x. solving we get 9.6 which is 9 +.6 of an
Hour =9.36 am.
4.A man sold 2 pens. Initial cost of each pen was Rs. 12. If he sell it together one at 25% profit and
Another 20% loss. Find the amount of loss or gain, if he sells them separately.
Answer: 60 Paisa losses
CP1= [1/ (1+.25)]*12 = Rs 9.60
CP2= [1/] 1-.20)]*12 = Rs 15
Selling together -CP1+CP2 = Rs.24.60
Selling separately- 12+12 = Rs .24
Loss=60 paisa.
5.A boy asks his father, “what is the age of grand father?". Father replied " He is x years old in x^2 years", and also said, "we are talking about 20th century". What is the year of birth of grand father?
Answer: 1892
44*44=1936
Therefore 44 years old in 1936 so year of birth=1936-44=1892
6.A boy travels in a scooter after covering 2/3rd of the distance the wheel got punctured he covered the remaining distance by walk. Walking time is twice that of the time the boy’s riding time. How many times the riding speed as that of the walking speed?
Answer: 4 times.
X-total distance to be traveled
[2/3(x)]/a =T1 (a-ridding speed, T1-ridding time)
[1/3(x)]/b =T2 (b-walking speed T2- walking time)
T2=2T1
Equating we will get a=4b
7.In a Knockout tournament 51 teams are participated, every team thrown out of the tournament if they lost twice. How many matches to be held to choose the winner?
Ans: 101 matches
2n-1=2(51)-1=102-1=101
8. One-third of the persons in front of me together with 3/4th of the persons behind me equals the total number of the persons in the merry go round. Find the total number.
Answer:
(number in front = number behind = total number -1)
so,
(1/3)(n-1) + (3/4)(n-1) = n
n=13
9. A bus has a maximum speed of 100 km/h. With 3 people, the bus moves at a speed of 88 km/h. With 6 people what would be the velocity if the bus' speed decreases proportionately with the number of people in the bus.
Answer:
At 100 kmph, only driver is in the bus.
Persons speed
1 100
1+2 100 - 6*2 = 88 kmph
1+5 100 - 6*5 = 70 kmph
10. In an island, natives always lie and visitors always tell the truth. I met a salesman in a hotel in the island. I wanted to know whether the salesman was a native or a visitor. For that, instead of directly asking him, I asked him to ask a woman sitting in the nearby table whether she is a native or a visitor. The salesman asked the woman and said" she said she is a visitor". Is it possible to find whether the salesman was a visitor or a native? If so, what is he?
Answer:
The possible combinations for the salesman and the woman are
salesman woman
1. T T (Y)
2 F T (N)
3. T F (Y)
4. F F (N)
if 4,
then woman and salesman should have lied. so, the woman should
have said "i am a native", but she would be a visitor.(contradictory with
assumption that W-F)
if 3,
then woman had lied and salesman says the truth. So, the woman
should have said "i am a visitor", but she was a native. (Acceptable)
if 2,
then woman says the truth and salesman lied. So the woman should
have said "i am a native" , but she was a visitor.(contradictory with
assumption that W-T)
if 1,
then woman and salesman say the truth. so both are visitors.
(acceptable).
so, only 1 and 3 are acceptable (T, T) and (T,F). In both cases,
the salesman says the truth and is a visitor.
11. A 1 k.m. long wire is held by n poles. If one pole is removed, the length of the gap increases by 5/3 meters. What is the number of poles initially?
Answer:
if n poles,
(n-1) gaps of each 1000/(n-1) width
if n-1 poles,
(n-2) gaps of each 1000/(n-2) width
so,
1000/(n-2) - 1000/(n-1) = 5/3
1000(1/(n-2) -1/(n-1)) = 5/3
1000(1/((n-1)(n-2))) = 5/3
(n-1)(n-2) =(3/5) * 1000 = 600
as 600 = 25 * 24
n-1 = 25, n=26 poles
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