28 - 45
28. There is a safe with a 5 digit number as the key.
The 4th digit is 4 greater than second digit,
while 3rd digit is 3 less than 2nd digit.
The 1st digit is thrice the last digit.
There are 3 pairs whose sum is 11.
Find the number.
65292
Couldnt find any proper method to solve except to trial and error.
29. Three friends divided some bullets equally. After all of them shot 4 bullets the total number of bullets remaining is equal to the bullets each had after division. Find the original number divided
Let initial be X bullets.
so each ones share is X/3.
each shot 4 bullets so we have (X - 12) = X / 3
X = 18
30. Father's age is three years more than three times the son's age. After three years, father's age will be ten years more than twice the son's age. What is the father's present age?
Let fathers age be X and sons age be Y
X = 3Y + 3
X + 3 = 2(Y + 3) + 10
solving we get X = 33 and Y = 10
31. How can 1000000000 be written as a product of two factors neither of them containing zeros
Ans: 2 power 9 x 5 power 9
Flicked the solution off the internet but this seems to be cool. :-)
32. Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination 1 hr and 4 hours respectively after passing each other. How much faster is one train from other.
Distance travelled is same. Let total distance be D. Let meeting point be X kms.
Lets assume Train A travels from Bangalore to Mysore and Train B from Mysore to Bangalore.
Let S1 be speed of train A and S2 be speed of train B
so (D - X) / S1 = 1 hour.
X / S2 = 4 Hours.
Also D/ S1 - D/S2 = 3 hours.
Solving we get S1 is twice as fast as S2.
33. A man collects cigarette stubs and makes one full cigarette with every 8 stubs. If he gets 64 stubs how many full cigarettes can he smoke?
8 + 1 = 9.
34. Two trains start from stations A and B spaced 50kms apart at the same time and speed. As the trains start, a bird flies from one train towards the other and on reaching the second train, it flies back to the first train. This is repeated till the trains collide. If the speed of the trains is 25 km/h and that of the bird is 100km/h. How much did the bird travel till the collision.
The trains take 1 hour to collide. So the bird would have travelled 100 km as the speed of
the bird is 100 Kmph.
35. There are 6 volumes of books on a rack kept in order ( i.e. vol.1, vol. 2 and so on ). Give the position after the following changes were noticed.
1. Vol.5 was directly to the right of Vol.2
2. Vol.4 has Vol.6 to its left and both weren't at Vol.3's place
3. Vol.1 has Vol.3 on right and Vol.5 on left
4. An even numbered volume is at Vol.5's place
Find the order in which the books are kept now
251364
36. First : I have three children. The product of their ages is 36. If you sum their ages,
it is exactly same as my neighbor's door number on my left.
The second mathematician verifies the door number and says that it is not sufficient. Then the first says " Ok one more clue is that my youngest is really the youngest". Immediately the second mathematician answers. Can you answer the question asked by the first mathematician? What are the children ages?
36 can be split into 2 * 2 * 9 or 4 * 3 * 3 or 1 * 6 * 6
the second clue says the he has only one younger kid so that leave us 1 * 6 * 6
37. I bought a car with a peculiar 5 digit numbered license plate which on reading upside down could still be read. On reading upside down the value is increased by 78633.Whats the original number if
all digits were different?
0 1 6 8 9 are the nos which make sense when reading upside down.
Difference in the first and last digit is 7 and 3 so 8 and 1 fit the first and last digit.
second digit also has differnce of 3 so 0 and 6 fit the profile. so only left out is 9.
so origninal no is 10968
38. 9 cards are there. u have to arrange them in a 3*3 matrix.
cards are of 4 colors.they are red,yellow,blue,green.
conditions for arrangement: one red card must be in first row
or second row.2 green cards should be in 3rd column.Yellow
cards must be in the 3 corners only. Two blue cards must be in
the 2nd row. Atleast one green card in each row.
Total Color Condition
3 Green 2 cards should be on the third column and 1 card per row.
3 Yellow Cards in corners only.
2 Blue cards in 2nd row.
1 Red 1 or 2 row.
Y R G
B B G
Y G Y
39. A family I know has several children. Each boy in this
family has as many sisters as brothers but each girl has
twice as many brothers as sisters. How many brothers
and sisters are there
Let x be no of boys and y be no of girls.
x - 1 = y
2(y - 1) = x
solving we get x = 4 and y = 3
40. No. of animals (assume 4 legs) is 11 more than the no. of birds. If the
no. of birds were the no. of animals and no. of animals
were the no. of birds( ie., interchanging no.s of animals
and birds.), the total no. of legs get reduced by one fifth
(1/5). How many no. of birds and animals were there?
Let x be the no of animals and y be the no of birds.
x - y = 11
y*4 + x*2 = (x*4 + y*2) * 4 / 5
solving we get x = 22 and y = 11
41.
Lets call the Nos multiplied A and B.
The last digit of B is 2 as we have the product step first no as 5.
The second digit of A should be greater than 5 as there is a carry forward.
The last digit of A is 1 as the product with B in step 3 gives the same.
The second digit of B is likely to be 3 or 4 as we have the product still a 3 digit no
and 2 digit > 5. so choosing 3 and 8 or 4 and 6 we can get the digit 4. but 4-6 leads
to 4 digit no so we have to choose 3 and 8. so the nos are
281 and 332.
42. TANVEER AND KUNAL WENT DOWN A DESCENDING ESCALATOR . THE ESCALATOR
WAS GOING DOWN AT A CONTANT SPEED . KUNAL WALKED DOWN THE STEPS AND
HAD TO COVER 50 STEPS TO REACH THE BOTTOM.TANVEER ON THE OTHER HAND , RAN
DOWN THE STEPS OF THE ESCALATOR AND HENCE HAD TO TAKE 75 STEPS TO REACH
THE BOTTOM . ACTUALLY , TANVEER TOOK 3 STEPS IN THE SAME TIME IT TOOK
KUNAL TO TAKE 1 STEP . HOW MANY STEPS WOULD BE visible when the ecalator
is stopped and not operating.?
Let X be the constant rate of the escalator.
Let N be the no of steps.
Time taken by kunal to come down = (N - 50)/ X
Time taken by tanveer to come = (N - 75)/ X
time taken by kunals one step = 3 * time taken by tanveers step.
(N - 50)/ 50X = 3 * (N - 75) / 75X
solving we get N = 100
43. Four perssons are three to cross a bridge they have one torch light
one person A can cross in 1 min
person B can cross in 2 min
person C can cross in 5 min
person D can cross in 10 min
They have to cross bridge with in 17 min.
At a time only two persons can cross
I A&B ----> 2
II A <----1
III C&D ---->10
IV B <----2
V A&B ---->2
__________
Total 17
44. Three are three boxes ,
In one box Two white balls
In two box 2 black balls
In three box 1 white &1 black
The lables on the boxes are not correct.Then you have to open
one box and to find the colour of the balls in all boxes.
Open the box labelled 1 white and 1 Black it has either black balls/ White balls
paste the label for that and switch the other 2.
45. A frog jumps 3 ft falls back 2ft in a day.how many days
will it take to come out of 30ft deep well?
First 27 days it gains 1 feet 28th day it climbs 3 feet coming out.
The 4th digit is 4 greater than second digit,
while 3rd digit is 3 less than 2nd digit.
The 1st digit is thrice the last digit.
There are 3 pairs whose sum is 11.
Find the number.
65292
Couldnt find any proper method to solve except to trial and error.
29. Three friends divided some bullets equally. After all of them shot 4 bullets the total number of bullets remaining is equal to the bullets each had after division. Find the original number divided
Let initial be X bullets.
so each ones share is X/3.
each shot 4 bullets so we have (X - 12) = X / 3
X = 18
30. Father's age is three years more than three times the son's age. After three years, father's age will be ten years more than twice the son's age. What is the father's present age?
Let fathers age be X and sons age be Y
X = 3Y + 3
X + 3 = 2(Y + 3) + 10
solving we get X = 33 and Y = 10
31. How can 1000000000 be written as a product of two factors neither of them containing zeros
Ans: 2 power 9 x 5 power 9
Flicked the solution off the internet but this seems to be cool. :-)
32. Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination 1 hr and 4 hours respectively after passing each other. How much faster is one train from other.
Distance travelled is same. Let total distance be D. Let meeting point be X kms.
Lets assume Train A travels from Bangalore to Mysore and Train B from Mysore to Bangalore.
Let S1 be speed of train A and S2 be speed of train B
so (D - X) / S1 = 1 hour.
X / S2 = 4 Hours.
Also D/ S1 - D/S2 = 3 hours.
Solving we get S1 is twice as fast as S2.
33. A man collects cigarette stubs and makes one full cigarette with every 8 stubs. If he gets 64 stubs how many full cigarettes can he smoke?
8 + 1 = 9.
34. Two trains start from stations A and B spaced 50kms apart at the same time and speed. As the trains start, a bird flies from one train towards the other and on reaching the second train, it flies back to the first train. This is repeated till the trains collide. If the speed of the trains is 25 km/h and that of the bird is 100km/h. How much did the bird travel till the collision.
The trains take 1 hour to collide. So the bird would have travelled 100 km as the speed of
the bird is 100 Kmph.
35. There are 6 volumes of books on a rack kept in order ( i.e. vol.1, vol. 2 and so on ). Give the position after the following changes were noticed.
1. Vol.5 was directly to the right of Vol.2
2. Vol.4 has Vol.6 to its left and both weren't at Vol.3's place
3. Vol.1 has Vol.3 on right and Vol.5 on left
4. An even numbered volume is at Vol.5's place
Find the order in which the books are kept now
251364
36. First : I have three children. The product of their ages is 36. If you sum their ages,
it is exactly same as my neighbor's door number on my left.
The second mathematician verifies the door number and says that it is not sufficient. Then the first says " Ok one more clue is that my youngest is really the youngest". Immediately the second mathematician answers. Can you answer the question asked by the first mathematician? What are the children ages?
36 can be split into 2 * 2 * 9 or 4 * 3 * 3 or 1 * 6 * 6
the second clue says the he has only one younger kid so that leave us 1 * 6 * 6
37. I bought a car with a peculiar 5 digit numbered license plate which on reading upside down could still be read. On reading upside down the value is increased by 78633.Whats the original number if
all digits were different?
0 1 6 8 9 are the nos which make sense when reading upside down.
Difference in the first and last digit is 7 and 3 so 8 and 1 fit the first and last digit.
second digit also has differnce of 3 so 0 and 6 fit the profile. so only left out is 9.
so origninal no is 10968
38. 9 cards are there. u have to arrange them in a 3*3 matrix.
cards are of 4 colors.they are red,yellow,blue,green.
conditions for arrangement: one red card must be in first row
or second row.2 green cards should be in 3rd column.Yellow
cards must be in the 3 corners only. Two blue cards must be in
the 2nd row. Atleast one green card in each row.
Total Color Condition
3 Green 2 cards should be on the third column and 1 card per row.
3 Yellow Cards in corners only.
2 Blue cards in 2nd row.
1 Red 1 or 2 row.
Y R G
B B G
Y G Y
39. A family I know has several children. Each boy in this
family has as many sisters as brothers but each girl has
twice as many brothers as sisters. How many brothers
and sisters are there
Let x be no of boys and y be no of girls.
x - 1 = y
2(y - 1) = x
solving we get x = 4 and y = 3
40. No. of animals (assume 4 legs) is 11 more than the no. of birds. If the
no. of birds were the no. of animals and no. of animals
were the no. of birds( ie., interchanging no.s of animals
and birds.), the total no. of legs get reduced by one fifth
(1/5). How many no. of birds and animals were there?
Let x be the no of animals and y be the no of birds.
x - y = 11
y*4 + x*2 = (x*4 + y*2) * 4 / 5
solving we get x = 22 and y = 11
41.
2 * * |
3 * * | No. 7 does not occur in this
---------------- |
5 * * | multiplication.
* 4 * |
* * 3 | Find the product.
---------------- |
* * * * * |
---------------- |
Lets call the Nos multiplied A and B.
The last digit of B is 2 as we have the product step first no as 5.
The second digit of A should be greater than 5 as there is a carry forward.
The last digit of A is 1 as the product with B in step 3 gives the same.
The second digit of B is likely to be 3 or 4 as we have the product still a 3 digit no
and 2 digit > 5. so choosing 3 and 8 or 4 and 6 we can get the digit 4. but 4-6 leads
to 4 digit no so we have to choose 3 and 8. so the nos are
281 and 332.
42. TANVEER AND KUNAL WENT DOWN A DESCENDING ESCALATOR . THE ESCALATOR
WAS GOING DOWN AT A CONTANT SPEED . KUNAL WALKED DOWN THE STEPS AND
HAD TO COVER 50 STEPS TO REACH THE BOTTOM.TANVEER ON THE OTHER HAND , RAN
DOWN THE STEPS OF THE ESCALATOR AND HENCE HAD TO TAKE 75 STEPS TO REACH
THE BOTTOM . ACTUALLY , TANVEER TOOK 3 STEPS IN THE SAME TIME IT TOOK
KUNAL TO TAKE 1 STEP . HOW MANY STEPS WOULD BE visible when the ecalator
is stopped and not operating.?
Let X be the constant rate of the escalator.
Let N be the no of steps.
Time taken by kunal to come down = (N - 50)/ X
Time taken by tanveer to come = (N - 75)/ X
time taken by kunals one step = 3 * time taken by tanveers step.
(N - 50)/ 50X = 3 * (N - 75) / 75X
solving we get N = 100
43. Four perssons are three to cross a bridge they have one torch light
one person A can cross in 1 min
person B can cross in 2 min
person C can cross in 5 min
person D can cross in 10 min
They have to cross bridge with in 17 min.
At a time only two persons can cross
I A&B ----> 2
II A <----1
III C&D ---->10
IV B <----2
V A&B ---->2
__________
Total 17
44. Three are three boxes ,
In one box Two white balls
In two box 2 black balls
In three box 1 white &1 black
The lables on the boxes are not correct.Then you have to open
one box and to find the colour of the balls in all boxes.
Open the box labelled 1 white and 1 Black it has either black balls/ White balls
paste the label for that and switch the other 2.
45. A frog jumps 3 ft falls back 2ft in a day.how many days
will it take to come out of 30ft deep well?
First 27 days it gains 1 feet 28th day it climbs 3 feet coming out.
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