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Grand Father, Father and Grand Son Ages

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One grand father
One father
One Grand Son
Sum of their ages is 140 years
Grand son’s age in month
is equal to grand fathers age in years
Grand son’s age in days
is equal to Father’s age in weeks
Now, Find out the age of all three.

Check your answer:-

Grand son’s age in years

Tried enough already?

Father’s age in years

Tried enough already?

Grand father’s age in years

Tried enough already?


Click here to See Answers
Lets say G, F and S are ages of grand father, father and son in years
than
G+F+S = 140
S*12 = G
S*365 = (F*365)/7 => F = 7S
Than 12S + 7S + s = 140 => 20S = 140 => S = 7 Years
F = 49 Years
G = 84 Years

Tyres on the bus

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Number Puzzle #93
If 8 tyres were used on a bus (with 6 tyres) which traveled 16000 km.
How many km did each tyre sustain?
Note: all the tyres were used equally in sustaining this distance.


Check your answer:-

Tried enough already?
Click here to See Solution
Sum of the distance traveled by all tyres = 6*16000 = 96000
Distance traveled by each tyre = 96000/8 = 12000.

How many toys?

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Number Puzzle #90

A man had Rs.900 and brought some toys with all the money. Out of which 5 toys were defected. He sold all the remaining toys by increasing the price by Rs.2 and made a profit of Rs.80.
What is the no.of initial toys and the initial cost of toys?

Check your answer, Number of Toys:-

Tried enough already?

Check your answer, Initial Cost:-

Tried enough already?
Click here to See Solution
Let assume he had x toys and bought it for Rs.y per piece.
Now, we can form these two equations from these
x*y = 900;//Total cost
(y+2)(x-5) = 900+80;//as he mad profit of Rs.80 by selling x-5 toys in Rs.(y+2).

xy + 2x -5y -10= 900+80;
2x-5y = 90;
2x-5*900/x = 90
2x^2 -4500 = 90x;
x^2 -45x – 2250 = 0;
(x-75)(x+30) = 0;
x = 75 and x =–30, as number of toys cant be negative, initial number of toys were 75.
Initial Cost = 900/75 = Rs.12.

Magic Trick Solution – Google Code Jam 2014

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Google Code Jam 2014 has begun, You need to get 25 points to get to the next round, there are 4 problems out of which two problems needs to be solved for sure to get into next round.

This is the first problem and the most simpler one and gives you only 6 points 🙁

Problem

Recently you went to a magic show. You were very impressed by one of the tricks, so you decided to try to figure out the secret behind it!

The magician starts by arranging 16 cards in a square grid: 4 rows of cards, with 4 cards in each row. Each card has a different number from 1 to 16 written on the side that is showing. Next, the magician asks a volunteer to choose a card, and to tell him which row that card is in.
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Product of 5 different temperatures

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Number Puzzle #66
The product of 5 different temperatures is 12. If all of them are integers then find all the temperatures.


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product of 5 different integers is 12.

Lets consider first product of first 3 smallest integers
1*2*3 = 6
Now if we take the next smallest intege i.e. 4 then the product will become 24 thus we need to go back and consider negative numbers

thus (-2)*(-1)*1*2*3 = 12.

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