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Tuesday, 10 March 2009 21:12 |
A three digit number consists of 9, 5 and one more number. When these digits are reversed and then subtracted from the original number the answer yielded will be consisting of the same digits arranged yet in a different order. What is the other digit?
Let the digit unknown be n.
The given number is then 900+50+n=950+n.
When reversed the new number is 100n+50+9=59+100n.
Subtracting these two numbers we get 891-99n.
The digit can be arranged in 3 ways or 6 ways.
We have already investigated 2 of these ways.
We can now try one of the remaining 4 ways. One of these is n 95
100n+90+5=891-99n
Or 199n =796
So, n=4
The unknown digit is 4
Five houses lettered A,B,C,D, & E are built in a row next to each other. The houses are lined up in the order A,B,C,D, & E. Each of the five houses has a colored chimney. The roof and chimney of each house must be painted as follows.
> The roof must be painted either green, red ,or yellow.
> The chimney must be painted either white, black,or red.
>No house may have the same color chimney as thecolor of roof.
>No house may use any of the same colors that theevery next houseuses.
>House E has a green roof.>House B has a red roof and a black chimney
1. Which of the following is true ?
(a) At least two houses have black chimney.
(b) At least two houses have red roofs.
(c) At least two houses have white chimneys.
(d) At least two houses have green roofs
(e) At least two houses have yellow roofs
2. Which must be false ?
(a) House A has a yellow roof
(b) House A & C have different color chimney
(c) House D has a black chimney
(d) House E has a white chimney
(e) House B&D have the same color roof.
3. If house C has a yellow roof. Which must be true?
(a) House E has a white chimney
(b) House E has a black chimney
(c) House E has a red chimney
(d) House D has a red chimney
(e) House C has a black chimney
Solution: 1(c), 2(b), 3(a)
Four horses are tethered at 4 corners of a square field of side 70 meters so that they just cannot reach one another. The area not grazed by the horses is ?
The length of the rope in which the horses tied should be equal to half of the side of the square plot so that they just cannot reach one another. Therefore, the length of the rope is 35m (70/2).
The area covered by each horse should be equal to the area of sector with radius of 70/2 = 35m (length of the rope).
Total area covered by the four horses = 4* area of sector of radius 35 meters = Area of circle of radius 35m.
Area not grazed by the horses = Area of square field - Area covered by four horses.
= 702 - (22/7)*35*35 = 4900 - 3850 = 1050 sq.m.
A 20 liter mixture of milk and water contains milk and water in the ratio 3: 2. 10 liters of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removals and replacement, what is the ratio of milk and water in the resultant mixture?
The 20 liter mixture contains milk and water in the ratio of 3: 2. Therefore, there will be 12 liters of milk in the mixture and 8 liters of water in the mixture.
Step 1- When 10 liters of the mixture is removed, 6 liters of milk is removed and 4 liters of water is removed. Therefore, there will be 6 liters of milk and 4 liters of water left in the container. It is then replaced with pure milk of 10 liters. Now the container will have 16 liters of milk and 4 liters of water.
Step 2- When 10 liters of the new mixture is removed, 8 liters of milk and 2 liters of water is removed. The container will have 8 liters of milk and 2 liters of water in it. Now 10 liters of pure milk is added. Therefore, the container will have 18 liters of milk and 2 liters of water in it at the end of the second step.
Therefore, the ratio of milk and water is 18: 2 or 9: 1.
If widowers and divorced males retained their group they had upon marrying which of the following would be permissible (Assume that no previous marriage occurred)
(A) A woman marrying her dead sister's husband
(B) A woman marrying her divorced daughter'sex-husband
(C) A widower marrying his brother's daughter
(D) A woman marrying her mother's brother who is awidower.
Ans. D
A group of workers can do a piece of work in 24 days. However as 7 of them were absent it took 30 days to complete the work. How many people actually worked on the job to complete it?
Let the original number of workers in the group be 'x'. Therefore, actual number of workers = x-7.
We know that the number of man hours required to do the job is the same in both the cases.
Therefore, x (24) = (x-7).30 24x = 30x - 2106x = 210x = 35.
Therefore, the actual number of workers who worked to complete the job = x - 7 = 35 -7 = 28
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