Maths Riddles

14
If the begger can make a whole cigarette from 6 butts then he can make 12 cigarettes from the 72 he found. Once he smokes those, he then will have another 12 butts, which gives him enough to make another 2 cigarettes. A total of 14.

the farmer needs 3 hens to produce 12 eggs in 6 days

This is a classic problem that many people get wrong because they reason that half of a hen cannot lay an egg, and a hen cannot lay half an egg. However, we can get a satisfactory solution by treating this as a purely mathematical problem where the numbers represent averages.

To solve the problem, we first need to find the rate at which the hens lay eggs. The problem can be represented by the following equation, where RATE is the number of eggs produced per hen·day:

1½ hens × 1½ days × RATE = 1½ eggs

We convert this to fractions thus:
3/2 hens × 3/2 days × RATE = 3/2 eggs

Multiplying both sides of the equation by 2/3, we get:
1 hen × 3/2 days × RATE = 1 egg

Multiplying both sides of the equation again by 2/3 and solving for RATE, we get:
RATE = 2/3 eggs per hen·day

Now that we know the rate at which hens lay eggs, we can calculate how many hens (H) can produce 12 eggs in six days using the following equation:

H hens × 6 days × 2/3 eggs per hen·day = 12 eggs

Solving for H, we get:
H = 12 eggs /(6 days × 2/3 eggs per hen·day) = 12/4 = 3 hens

Therefore, the farmer needs 3 hens to produce 12 eggs in 6 days.

The digits are 12, 5, 6, and 8

Katrina

As noted, all three are 140 years old. Thus, a+b+c=140, where a is grandfather, b is son, and c is grandson. Additionally, grandson being about as many days old as son is in weeks gives 365c=52b. Finally, the grandson being as many months as I am in years gives 12c=a. Thus, the following are known.

a+b+c=140
365c=52b or b=365c/52
12c=a

By calculation and substitution we have as follows.

12c + 365c/52 +c = 140
624c + 365c + 52c = 7280
1041c = 7280
c = 6.99, or 7 (teaser said 'about')
so, as 12c = a, then a = 84.

I am 84 years old.
As an aside, my son is 49

Just 1

Pooja had 50pound and Neha had 30 pound.
Pooja Neha
50 30
20 60
40 40
0 80

44 and 66

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

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.