The difference between two numbers is 5 and the difference between their square is 65. What is the smaller number?
Solution
Correct Answer: Option A
Let the numbers be x and y
Then,
x - y = 5.........(i)
x2 - y2 = 65
Or (x + y)(x - y) = 105
5(x + y) = 65
x + y = 13 ....... (ii)
by adding (i) and (ii) we get,
2x = 5 + 13
2x = 18
x = 9
From (ii) we get
x + y = 13
9 + y = 13
y = 13 - 9
y = 4
Hence, the smaller number is 4
Then,
x - y = 5.........(i)
x2 - y2 = 65
Or (x + y)(x - y) = 105
5(x + y) = 65
x + y = 13 ....... (ii)
by adding (i) and (ii) we get,
2x = 5 + 13
2x = 18
x = 9
From (ii) we get
x + y = 13
9 + y = 13
y = 13 - 9
y = 4
Hence, the smaller number is 4
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