Aptitude Test 1 :
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In the given number, we have the first five natural numbers in ascending order up to 5.
After 5, we have the first four natural numbers in descending order.
Whenever we have a number like this and we want to find square root, we have to replace each digit by 1, up to the digit where we have the first n natural natural numbers in ascending order.
So, in our number 123454321, we have to replace each digit by 1 up to 5. That is the square root of 123454321.
Hence the square root of 123454321 is 11111.
Total distance covered to cross each other = 100 + 80 = 180 m
(when they run in opposite direction or same direction)
Relative speed of the two trains = 60-18 = 12 kmph (running in the same direction)
= 12X5/18 = 10/3 m/sec
Time taken to cross each other = Distance/Speed
= 180/(10/3) seconds
Hence, time taken to cross each other = 54 seconds.
The work has to completed in 90 days (as per schedule)
Total no. of men appointed initially = 50
50 men worked 20 days and completed a part of the work
The remaining work is completed by 70 men (50+20=70) in 70 days (90-20=70)
If the remaining work is completed by 50 men,
no. of days taken by them = (70X70)/50 = 98 days.
Hence, extra days needed = 98-70 = 28 days.
From the given information, Already 3 km distance (one half of the distance 6km) has been covered in 30 minutes or 1/2 hr. (two third of the total time 45 minutes)
Remaining distance = 3 km
Time available = 15 minutes or 1/4 hr
Speed required = Distance / Time
= 3/(1/4) kmph = 3X4 kmph = 12 kmph
Hence, speed required to cover remaining distance is 12 kmph
Ten years ago, age of John and his father are x and 5x
Then, present age of John and his father are (x+10) and (5x+10)
John's age after six years will be three-seventh of his father's age
(x+10+6) = 3/7(5x+10+6)
(x+16) = 3/7(5x+16)
7(x+16) = 3(5x+16)
Solving the above equation, we get x=8
Present age of John's father = 5x+10
plug x = 8
Present age of John's father = 5(8)+10= 50 yrs
Let "x" be John's weight
According to Robert, we have 65 < x < 72
According to his brother, we have 60 < x < 70
According to his mother, we have x≤68
The values of "x" which satisfy all the above three conditions are 66, 67 and 68
Average of the above three values = (66+67+68)/3 = 201/3 = 67 kg
Hence average of different probable weights of Robert is 67 kg
Let "x" mph be speed in still water and "y" mph be speed of the current.
Then, speed downstream = (x+y) mph
By simplification, we get
x2 = y2+4y ----(1)
If the speed is doubled, speed in still water = 2x and speed of the current is same "y".
Speed down stream = (2x+y) mph and speed up stream = (2x-y) mph
12/(2x-y) - 12(2x+y) = 1
By simplification, we get
x2 = (24y+y2)/4 ----(2)
Solving (1) and (2), we get y = 8/3 = 22⁄3 mph
Hence speed of the current = 22⁄3 mph
From the given information,
Income of the 1st person = 4x
Income of the 2nd person = 5x
Expenditure of the 1st person = 4x-50
Expenditure of the 2nd person = 5x-50
(Because each saves $50 per month and Expenditure = Income - Savings)
Expenditure ratio = 7:9
(4x-50):(5x-50) = 7:9
9(4x-50) = 7(5x-50)
36x-450 = 35x-350
x = 100
Hence income of the second person = 5X100 = $500
Let the cost price of 1 liter pure milk be $1
Milk in 1 liter mixture in the 1st can = 3/4 (that is 75%)
Milk in 1 liter mixture in the 2nd can = 1/2 (that is 50%)
Milk in 1 liter mixture in the final mix = 5/8
(from the given ratio w:m = 3:5)
C.P of 1 liter mixture in the 1st can (c) = $3/4
C.P of 1 liter mixture in the 2nd can (d) = $1/2
C.P of 1 liter mixture in the final mix (m) = $5/8
Rule to find the ratio for producing mixture = (d-m):(m-c)
(d-m):(m-c) = 1/2-5/8:5/8-3/4 = 1/8:1/8 = 1:1
The above found ratio 1:1 says that equal quantity of milk should be taken from each of the cans.
Since he wants to get 12 liters of milk, he should take 6 liters of milk from each of the cans.
The correct answer is option (B) (6,6).
Let 100 tons be the production of wheat in 1994
In 1994 ===> 100 tons
In 1994-1995 ===> 120 tons (20% increment)
In 1995-1996 ===> 150 tons (further 25% increment)
When we look in to the above calculations, it is very clear that the production of wheat has been increased by 50 tons in 1996 from 100 tons in 1994
Percentage change = (50/100)X100 % = 50%
Hence, the percentage change in the production of wheat from 1994 to 1996 was 50%
After having practiced answering the above questions, we hope that the students would have understood, how to solve quantitative problems easily.
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