There is a shortage of tubelights, bulbs and fans in a village - Kharghar. It is found that
What percentage of houses do not have tubelight, bulb and fan?
Answer
42% houses do not have tubelight, bulb and fan.
Let's assume that there are 100 houses. Hence, there should be total 300 items i.e. 100 tubelights, 100 bulbs and 100 fans.
From the given data, we know that there is shortage of atleast (67+83+73) 223 items in every 100 houses.
Also, exactly 19 houses do not have just one item. It means that remaining 81 houses should account for the shortage of remaining (223-19) 204 items. If those remaining 81 houses do not have 2 items each, there would be a shortage of 162 items. But total of 204 items are short. Hence, atleast (204-162) 42 houses do not have all 3 items - tubelight, bulb and fan.
Thus, 42% houses do not have tubelight, bulb and fan.
Mr. Subramaniam rents a private car for Andheri-Colaba-Andheri trip. It costs him Rs. 300 everyday.
One day the car driver informed Mr. Subramaniam that there were two students from Bandra who wished to go from Bandra to Colaba and back to Bandra. Bandra is halfway between Andheri and Colaba. Mr. Subramaniam asked the driver to let the students travel with him.
On the first day when they came, Mr. Subramaniam said, "If you tell me the mathematically correct price you should pay individually for your portion of the trip, I will let you travel for free."
How much should the individual student pay for their journey?
Answer
The individual student should pay Rs. 50 for their journey.
Note that 3 persons are travelling between Bandra and Colaba.
The entire trip costs Rs. 300 to Mr. Subramanian. Hence, half of the trip costs Rs. 150.
For Andheri-Bandra-Andheri, only one person i.e. Mr. Subramaniam is travelling. Hence, he would pay Rs. 150.
For Bandra-Colaba-Bandra, three persons i.e Mr. Subramaniam and two students, are travelling. Hence, each student would pay Rs. 50.
Substitute digits for the letters to make the following Division true
O U T
-------------
S T E M | D E M I S E
| D M O C
-------------
T U I S
S T E M
----------
Z Z Z E
Z U M M
--------
I S T
Note that the leftmost letter can't be zero in any word. Also, there must be a one-to-one mapping between digits and letters. e.g. if you substitute 3 for the letter M, no other letter can be 3 and all other M in the puzzle must be
Answer
C=0, U=1, S=2, T=3, O=4, M=5, I=6, Z=7, E=8, D=9
It is obvious that U=1 (as U*STEM=STEM) and C=0 (as I-C=I).
S*O is a single digit and also S*T is a single digit. Hence, their values (O, S, T) must be 2, 3 or 4 (as they can not be 0 or 1 or greater than 4).
Consider, STEM*O=DMOC, where C=0. It means that M must be 5. Now, its simple. O=4, S=2, T=3, E=8, Z=7, I=6 and D=9.
O U T 4 1 3
------------- -------------
S T E M | D E M I S E 2 3 8 5 | 9 8 5 6 2 8
| D M O C | 9 5 4 0
------------- -------------
T U I S 3 1 6 2
S T E M 2 3 8 5
---------- ----------
Z Z Z E 7 7 7 8
Z U M M 7 1 5 5
-------- --------
I S T 6 2 3
Also, when arranged from 0 to 9, it spells CUSTOMIZED.
At what time after 4.00 p.m. is the minutes hand of a clock exactly aligned with the hour hand?
Answer
4:21:49.5
Assume that X minutes after 4.00 PM minute hand exactly aligns with and hour hand.
For every minute, minute hand travels 6 degrees.
Hence, for X minutes it will travel 6 * X degrees.
For every minute, hour hand travels 1/2 degrees.
Hence, for X minutes it will travel X/2 degrees.
At 4.00 PM, the angle between minute hand and hour hand is 120 degrees. Also, after X minutes, minute hand and hour hand are exactly aligned. So the angle with respect to 12 i.e. Vertical Plane will be same. Therefore,
6 * X = 120 + X/2
12 * X = 240 + X
11 * X = 240
X = 21.8182
X = 21 minutes 49.5 seconds
Hence, at 4:21:49.5 minute hand is exactly aligned with the hour hand.
A soldier looses his way in a thick jungle. At random he walks from his camp but mathematically in an interesting fashion.
First he walks one mile East then half mile to North. Then 1/4 mile to West, then 1/8 mile to South and so on making a loop.
Finally how far he is from his camp and in which direction?
Answer
The soldier is 0.8944 miles away from his camp towards East-North.
It is obvious that he is in East-North direction.
Distance travelled in North and South directions
= 1/2 - 1/8 + 1/32 - 1/128 + 1/512 - 1/2048 + and so on... (a geometric series with r = (-1/4) )
(1/2) * ( 1 - (-1/4)n )
= ---------------------------
( 1 - (-1/4) )
= 1 / ( 2 * ( 1 - (-1/4) ) )
= 2/5
Similarly in East and West directions
= 1 - 1/4 + 1/16 - 1/64 + 1/256 - and so on... (a geometric series with r = (-1/4) )
(1) * ( 1 - (-1/4)n )
= ---------------------------
( 1 - (-1/4) )
= 1 / ( ( 1- (-1/4) )
= 4/5
So the soldier is 4/5 miles away towards East and 2/5 miles away towards North. So using right angled triangle, soldier is 0.8944 miles away from his camp.
Raj has a jewel chest containing Rings, Pins and Ear-rings. The chest contains 26 pieces. Raj has 2 1/2 times as many rings as pins, and the number of pairs of earrings is 4 less than the number of rings.
How many earrings does Raj have?
Answer
12 earrings
Assume that there are R rings, P pins and E pair of ear-rings.
It is given that, he has 2 1/2 times as many rings as pins.
R = (5/2) * P or P = (2*R)/5
And, the number of pairs of earrings is 4 less than the number of rings.
E = R - 4 or R = E + 4
Also, there are total 26 pieces.
R + P + 2*E = 26
R + (2*R)/5 + 2*E = 26
5*R + 2*R + 10*E = 130
7*R + 10*E = 130
7*(E + 4) + 10*E = 130
7*E + 28 + 10*E = 130
17*E = 102
E = 6
Hence, there are 6 pairs of Ear-rings i.e. total 12 Ear-rings