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What is name of father? #49

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What is the Father's name

Mother’s name is
Mrs. Sixty Two
Son’s name is
FIFTY TWO
Daughter’s name is
FORTY TWO
What is the name of the father?

IF
Mother’s name is
Mrs. SIXTY TWO

Son’s name is
FIFTY TWO

Daughter’s name is
FORTY TWO

What is the name of the father?

Check your answer:-

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See Explanation
As mother’s name is Mrs. Sixty two so father’s name should be Sixty two.

Peculiar two digit number #44

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Peculiar two digit number

There is a peculiar two digit number which is three times the sum of its digits.
Can you find the number?

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See Solution
Lets say the number is ab

ab = 3(a+b)
We can also write it as 
10a + b = 3*(a+b)
7a = 2b
a/b = 2/7

As it is given that it is a two digit number, so it can only be 27.

Boy with Toffee #42

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Boy with Toffees

A boy has few toffees with him, then comes one of his friend and they decide to share them equally and they are able to divide them without any toffee remaining. Then one more friend comes and they divide the toffees in 3 equal parts, then one more friend comes, they are still able to divide the toffees in 4 equal parts, then comes one more friend, they are still able to divide them equally, similarly they are able to divide it equally in 5 and 6 equal parts but not when they are 7 and decide to divide equally they are left with one extra toffee.
Can you tell the minimum number of toffees boy had initially ?

Tried enough already?
See Solution
Since, They are able to divide the toffees equally between 2,3,4,5 and 6 boys so the number of toffees must be a multiple of all of these.
To get the minimum number we should first get the Least Common Multiple of 2,3,4,5 and 5, i.e. 2^2.3^1.5^1 = 60.
Now lets divide it by 7, the remainder is = 4, so it cant be the answer, So we should try the next possible answer i.e. 120, divide it by 7, remainder = 1, so minimum number of toffees boy can have is 120.

9 digit number #46

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9 digit number puzzle

There is a 9 digit number. No digit are repeated and rightmost digit is divisible by 1 and right 2 digits is divisible by 2, right 3 digits is divisible by 3 and so on, finally the whole number is divisible by 9.

Can you find out the number?

See Solution
As the right two digits are divisible by 2, so rightmost digit should be even, at the same time right 5 digits are divisible by 5 so the rightmost digit can be 5 or 0, but as it should be even so it can only be 0.

Now, Right 4 digits are divisible by 4, so the rightmost two digits can be either 20, 40, 80 or 60.
To be divisible by 9 the digits of a number must sum to a multiple of 9. Adding the 10 digits together (0+1+2+…+8+9) gives 45 which is div by 9. However, this is a 9-digit number so we have to drop one from the ten. We can only take out 0 or 9 and still have the remaining digits sum to a multiple of 9. We’ve already shown that 0 is present so the 9 is dropped.
Right 3 digits are divisible by 3 so these 3 digits can be 120, 420, 720, 240, 540, 840, 180, 480, 780, 360.
Now to be divisible by 6 sum of the six digits should be divisible by 3 and it should also be even, which it is.

There is no rule for divisible by 7 so we just have to take digits such that they are divisible by 7, there can be many such numbers and one such number is 123567480.

Coins and sandwiches

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Three friends A, B and C went on a trip.
A didn’t carry any food with him but had 13 Coins. B had 6 sandwiches, and C had 7 sandwiches with him (Total 13 Sandwiches).

They decided to share the food equally and in return A would give away all 13 coins to B & C.

How should B & C distribute the money?


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Coins and sandwiches solution

Since they have to share the sandwiches equally, each of them will get 13/3 sandwiches.

Hence the sandwiched contributed by B and C to A.
B: 6 – 13/3 = 5/3
C:7 -13/3 = 8/3

Now A should give the money in the ratio of what he got from B and C, i.e.
5/3:8/3 :: 5:8

Hence B will get 5 and C will get 8 coins.

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