Solution:

Total Number of Matches: 63
Explanation:
32+16+8+4+2+1 = 63

Solution:

9+8+7+65+4+3+2+1+0

Solution:

The only number is 2592. 2^5 is 32 and 9^2 is 81. 32*81 is 2592.

Solution:

3:36 PM.
The clock loses 10 minutes each hour,
so it loses 5 minutes every half-hour,
and it loses 1 minute very 6 minutes.

It is 12:50 PM at 1:00 o'clock.
It is 1:40 PM at 2:00 o'clock.
It is 2:30 PM at 3:00 o'clock.
It is 2:55 PM at 3:30 o'clock.
It is 3:00 PM at 3:36 o'clock.

Solution:

In one hour,

Soln 1:
the large inlet tube fills 1 / 3 of the tank;
the small inlet tube fills 1 / 6 of the tank;
the outlet tube empties 1 / 9 of the tank; and therefore
all three tubes together fill [ (1 / 3) + (1 / 6) − (1 / 9) ] of the tank.

Fraction of the tank that will be filled in 0.64 hours =
0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25.


Soln 2:
Let V be the total volume of the tank. From equation (1),

Flow Rate (large inlet tube) = V / 3
Flow Rate (small inlet tube) = V / 6
Flow Rate (outlet tube) = V / 9.

Substituting in equation (2),

Rate of Accumulation in tank = (V / 3) + (V / 6) − (V / 9).

Using the above result in equation (1),

Time required to fill the complete tank = V / [ (V / 3) + (V / 6) − (V / 9) ].

Note that V cancels out on simplifying the above expression.

Fraction of the tank that will be filled in 0.64 hours =

0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25.

Solution:

47 + 53 + 59 + 61 = 220

Solution:

100/9 (fraction number is also a number)

lets say 'X' is the number.
10/X = X - 10
9X = 100
X = 100/9

Solution:

Lady:135 , Baby:25 & Dog:10

Solution:

The required number is 236 and the sum is 11.

It is given that the first two digits of the required number are prime numbers i.e. 2, 3, 5 or 7. Note that 1 is neither prime nor composite. Also, the third digit is the multiplication of the first two digits. Thus, first two digits must be either 2 or 3 i.e.
22, 23, 32 or 33 which means that there are four possible numbers - 224, 236,326 and 339.
Now, it is also given that - the difference between it's reverse and itself is 396.
Only 236 satisfies this condition. Hence, the sum of the three digits is 11.

Solution:

100. Looks hard? Don't worry, just work it backwards and you'll find it very easy.