A number is divided strictly into two unequal parts such that the difference of the squares of the two parts equals 50 times the difference between the two parts. What is the number?
a)45
b)50
c)65
d)35
Answers
A number is divided strictly into two unequal parts such that the difference of the squares of the two parts equals 50 times the difference between the two parts. What is the number?
answer : option (B) 50
solution : Let x and y are two parts of an unknown number. where x > y.
a/c to question,
the difference of the squares of the two parts equals 50 times the difference between the two parts.
i.e., (x² - y²) = 50(x - y)
or, (x - y)(x + y) - 50(x - y) = 0
[from algebraic identity, (a² - b²) = (a - b)(a + b) ]
or, (x - y) [(x + y) - 50] = 0
or, (x - y) ≠ 0 so, x + y - 50 = 0
⇒x + y = 50
hence, unknown number is (x + y) = 50.
The question is to find a number is divided strictly into two unequal parts such that the difference of the squares of the two parts equals 50 times the difference between the two parts.
Answer:
The answer is Option B) 50.
Explanation:
Let the two parts be x and y with x > y.
It is given that x^2 - y^2 = 50(x - y).
Hence,
(x + y) (x - y) = 50(x - y)
=> (x + y) (x - y) -50(x - y) = 0
=>(x - y) ((x + y)-50) = 0
It is given that both parts are unequal. Hence x - y cannot be equal to 0.
Therefore,
x + y -50 = 0.
=>Therefore, the number = x + y = 50.