Math Quiz - 1

Explanation
Moon is round because of formed and collapsed under the force of their own grLet B be 100. Then A is 120.
50% of B = 50
¾ of A = 90
Hence, 50% of B less than ¾ of A by 40.
Percentage: (40/90) x 100 = 44.44%

Explanation
Let the total work be 60 Units
X and Y : 12 days 5 units/day
Y and Z : 20 days 3 units/day
Y alone : 30 days 2 units/day
Using the above 3 relations,
X alone can do 5-2 = 3 units per day
Z alone can do 3-2 = 1 unit per day.
X,Y and Z together can do 2+3+1 = 6 units per day. Therefore, together they can do the work in 10 days.

Explanation
Let their present age be 8x and x respectively.
After 3 years, their age will be 8x+3 and x+3 respectively.
Difference in their age = 7x.
According to the problem 7x=4(x+3)
7x=4x+12
3x=12 or, x=4
Their present age will be 32 and 4 respectively.
3 years ago, their age would have been 29 and 1 respectively.
Required ratio will be 29:1.

Explanation
During the night the high contrast between the bright moon and the night's dark skies make theAccording to the problem,
Average age of the class = (2x17+3x19) /5
= (57+34)/5 = 91/5 = 18.2

Explanation
abc16 will give a remainder of 0 when divided by 4 and so the required last digit will be same as the
last digit of 8^4 = ie the last digit will be 6.

Explanation
It is given that CP of 6 items = SP of 5 items
Let the CP of one item be Rs. 5, then according to the given condition, SP of one item will be Rs. 6. Also, there is a 10% mark-up, which makes the SP (6+10% of 6) = 6.6. Now, Profit= (Rs. 6.6 - Rs.5)= Rs. 1.6.
Profit % = (1.6/5)x100% = 32%.

Explanation
The question says that no two boys are together. There is no restriction on two girls being together if possible.
The girls can be arranged in 3! ways.
_G_G_G_
Once the girls are seated(marked by G), there are 4 places(marked by underscore_) that the boys can occupy and they can do so in 4C3 x 3! ways = 4! ways.
Total number of ways = 3! x 4! ways.

Explanation
We will have to calculate from 1st January AD.
2000 years = 0 odd days.
Next 9 years will have:
2 leap years = 4 odd days and
7 ordinary years = 7 odd days
We need to include 1st January = 1 odd day.
Total number of odd days = 4 + 7 + 1 odd days = 12 odd days = 5 odd days.
Hence, 1st January 2010 will be a Friday.

Explanation
Distance to be covered = 150+100 = 250 m
Speed of the train = 90 kmph = 90x(5/18) m/sec = 25 m/sec.
Time taken for the train to cross the platform = 250/25 = 10 seconds.

Explanation
y:z = 4:5 and z is 15 more than y.
So, y will be 60 and z will be 75.
Now, x:y = 2:3 and so if y is 60, x will be 40.