. From a solid cylinder of height 10 cm and radius of the base 6 cm, a cone of same height and same base is removed. The volume of the remaining solid is?
A man starts cycling at 12.00 a.m. at a speed of 5kmph. A train A , starts running on a track with a speed of 100kmph at 5.00 a.m. Another train B, starts running on the adjacent parallel track with a speed of 120 kmph at 7.00 am from the same station and in the same direction. Find the distance travelled by the man when the two trains meet.
Let t be the time in hours after 5.00 am when the trains meet
Therefore distance covered
100 *t = 120 * (t-2)
I.e. the trains meet at 5pm till then the man cycles for 17 hours
Distance covered by the man =5*17=85 km
How many words can be made by using the letters of the word FRIEND if all the vowels should be3 at even places and no letter is repeated or left ?
We have six letters of which two are vowels. There are three even places where we can put two vowels in 3 * 2 ways = 6 ways
Remaining four places can be filled in 4*3*2*! = 24 ways
Hence, the number of words = 6*24 = 144 ways
Pipe A can fill a cistern in 36 minutes and B in 48 minutes. If both the pipes are simultaneously opened together , when should pipe B be closed so that the cistern maybe just full in 24minutes
Let pipe B be turned off after x minutes
Part filled in x minutes = x ( 1/36 + 1/48) = 7x/144
Part filled in 24-x minutes = (24-x) / 36
7x/144 + 24-x/36 = 1 HENCE x =16
A and B invest in a business in the ratio 3:2. if 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is:
The largest four digit number which when divided by 4,7 or 13 leaves a remainder of 3 in each case?
⇒ The largest 4 digit no is 9999
⇒ LCM of 4,7,13 is 364
⇒ Now divide 9999 by 364 and we get the remainder as 171
⇒ 4 digit divisible by 4,7,13=(9999-171)=9828
⇒ Now add the remainder 3 given in question (9828+3)
⇒ And answer is 9831.
In a game of Snooker, A can Give B 16 Points in 80 and A can Give C 15 point in 90. How many points can C give B in a game of 50?
In a game of billiards, A can give B 10 points in 60 and he can give C 15 in 60.How many points can B give C in a game of 90?
A scores 60 while B scores 50, and C scores 45.
. . B scores 90 while C scores 45/50 x 90 = 81
Hence, in a game of 90, B can give C ( 90-81) or 9 points .Let x points make the game, so that, according to the question,
if A has x points, then B has ( x-40) points.
B has x points, then C has ( x- 30) Points.
C has (x -64) points , then A has x points
. . By chain rule
x x ( x-64) = ( x- 40) ( x- 30)x
=> x2 - 64x = x2 - 70x + 1200
=> x = 2000
Hence, 200 points make the game
Rahul was 4 times old as his son 8 years back and he will be 2 times old as his son after 8 years. Calculate Rahul and his son's age?
Assume that currently it is year 2000.
In 1992 Rahul's age = 4x, Age of Rahul's son = x
In 2008 Rahul's age = 2y and Age of Rahul's son = y
Now we get two equations 2y - 4x = 16 and y - x = 16
By solving this equation x = 8, so Rahul' son's current age = 16 years and Rahul's age = 40 years
A container has got 130 liters of water which has 15% salt. From this container some of the water has got evaporated and after evaporation, the salt strength in the container is now 20%. Find out how much water evaporated from the container.