There is a peculiar two digit number which is three times the sum of its digits.
Can you find the number?
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.
A women was carrying a basket of Eggs when a passer-by bumped her and she dropped the basket and all the eggs broke, Passer-by asked her number of eggs to pay her. Women replied, I don’t remember exactly , but I do recall that whether I divided the eggs by 2,3,4,5 or 6 there was always one egg left over. When I took the eggs out in groups of seven, I emptied the basket.
Can you tell, “How many minimum number of Eggs were there in the basket”?
See SolutionA 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 ?
Average age of a 10 members committee is same as it was 4 years ago, because an old member is replaced by a younger member. What is difference between the younger member and the old member age.
Or in other words, how younger he is from his counterpart?
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 SolutionNow, 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.
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?
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.
3,7,5=>26
3,2,1=>5
2,8,6=>44
5,4,9=>?
Check your answer:-
See ExplanationIt was the first day of our second semester and we were looking for our hostel room numbers allotted, we saw that one of our friend was already allotted the room number last night and he challenged us to guess his new room number. We gave following answers
135, 780, 785 and 732.
He said, “That’s amazing”, “You’ve each guessed exactly one digit correctly and in its right place!”
Now can you guess what is his room number ?
See Guess the room number puzzle solution
Answer is 182
How?
The first digit must be 1 or 7. It can’t be 7 as only one digit is correct in each guess. So it’s 1.
The other digits in guess #1 (i.e. 3 and 5) must be incorrect. Therefore, from guess #3, the second digit is 8.
Guess #4 has a correct digit which must be its third, i.e. 2.
shopkeeper and duplicate note
A very simple but confusing puzzle.
A lady buys goods worth Rs.200 from a shop. (shopkeeper is selling the goods with zero profit). The lady gives him Rs.1000 note. The shopkeeper gets the change from the next shop and keeps Rs.200 for himself and returns Rs.800 to the lady. Later the shopkeeper of the next shop comes with the Rs.1000 note saying “duplicate” and takes his money back.
How much LOSS did the shopkeeper face?
Check your answer:-
See Shopkeeper and duplicate note solution
The answer is Rs.1000
How?
To get the loss of shopkeeper we can get the profit lady and the other shopkeeper.
Loss of first shopkeeper = (Profit of the lady + Profit of the second shopkeeper)
Profit of the lady = Rs.200(for goods) + Rs.800(for the change she received) = Rs.1000
Profit of the second shopkeeper = Rs.0(as he got his money back)
So the loss of the shopkeeper is = 1000 + 0 = Rs.1000
Second way of looking at is what shopkeeper gave to others and what is took from others
Loss of the shopkeeper = What he gave to others - what he took.
What he took
From Lady: Nothing(as the note was a duplicate one)
From Second Shopkeeper: Rs.1000
What he gave
To Lady:- Rs.200(goods) + Rs.800(change)
To second shopkeeper: Rs. 1000
So the loss = (200 + 800 + 1000) – (1000) = Rs.1000
IF 1 + 2 + 3 = 18
2 + 3 + 4 = 27
3 + 4 + 5 = 36
4 + 5 + 6 = 45
THEN: 5 + 6 + 7 = ??
Check your answer:-
See Explanation
