original numbers : x and y
each is increased by 10 ---> x+10 and y+10
percentage increase for first time = 10/x and 10/y
so new number is x+10 + 10/x
(same thing for the y)
x + 10 + 10/x = 72
times x
x^2 + 10x + 10 = 72x
x^2 - 62x = -10
completing the square:
x^2 - 62x + 961 = -10 + 961
(x - 31)^2 = 951
x - 31 = ± √951
x = 31 ± √951 = 61.838.. or .1617
check:
original number ---- 61.838
after adding 10 ---- 71.838
percentage increase = 10/61.838 = .1617..
which added to 71.838 = 72
same is true for .1617
your two numbers are 31+√951 and 31-√951
BUT, it said they are natural numbers, so there is no solution
Either my interpretation is incorrect or you have a typo
There are two distinct natural numbers. Each is first increased by 10 then by same percentage as each was increased for the first time. Each number finally results in 72 Find the difference between the numbers
Please explained in simplified way
5 answers
What I don't understand is how two distinct numbers, operated on in identical ways, produce the same result...
I think the question is mangled.
I think the question is mangled.
Hi Vipul,
let us consider the first number as x
X is increased by 10 - x+10
Then the increased number(x+10) is increased by a % which is equal to the percentage in the first calculation:-
%increase in first calculation : (10/x).
So the number should be increased by
(x+10)+(x+10)*(10/x) = 72
Solving these we get x = 50 or 2, which are the numbers.
let us consider the first number as x
X is increased by 10 - x+10
Then the increased number(x+10) is increased by a % which is equal to the percentage in the first calculation:-
%increase in first calculation : (10/x).
So the number should be increased by
(x+10)+(x+10)*(10/x) = 72
Solving these we get x = 50 or 2, which are the numbers.
How can equal percentage increase be 10/x?
Why
why is there 10/x ?
why is there 10/x ?
1 answer