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A number between 10 and 100 is five times the sum of its digits. If 9 be added to it the digits are reversed find the number.
- a)54
- b)53
- c)45
- d)55
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A number between 10 and 100 is five times the sum of its digits. If 9 ...
Let the number be 10 x + y
sum of its numbers = x+ y
according to the sum
10 x + y = 5(x + y)
10 x + y = 5 x + 5 y
10 x - 5 x = 5 y - y
5 x - 4 y = 0
if 9 is added the digits are reversed
⇒ 10 x + y + 9 = 10 y + x
10 x - x + 9 = 10 y - y
9 x - 9 y = - 9
x - y = - 1
simultaneous equation 5 x - 4 y = 0
x - y = -1
1(5 x - 4 y = 0)
5(x - y = -1)
5 x - 4 y = 0 →a
5 x - 5 y = -5→b
On subtracting b from a
5 x - 4 y = 0
- 5 x + 5 y = 5
y = 5
On substituting y = 5 in x - y = - 1
we get x = 4
The number is 10 x + y = 10(4) + 5 = 45
Most Upvoted Answer
A number between 10 and 100 is five times the sum of its digits. If 9 ...
Given information:
- A number between 10 and 100
- The number is five times the sum of its digits
- If 9 is added to the number, the digits are reversed
To find: The number
Solution:
Let's assume the number to be xy, where x and y are digits.
According to the given information, we have two equations:
1. xy = 5(x+y)
2. xy + 9 = 10y + x
Solving the equations:
From equation 1, we get:
xy = 5x + 5y
xy - 5x = 5y
x(y-5) = 5y
Since x and y are digits, y can't be zero. So, we can divide both sides by y:
x = 5 + 5/y
Since x is a digit, y can only be 1 or 5. But if y is 1, x will be a fraction which is not possible. So, y must be 5.
Putting y=5 in the above equation, we get:
x = 5 + 5/5 = 6
So, the number xy is 65.
Now, from equation 2, we have:
xy + 9 = 10y + x
65 + 9 = 10(5) + 6
74 = 56
But the digits are reversed, so the number must be 47.
Therefore, the correct option is (c) 45.
- A number between 10 and 100
- The number is five times the sum of its digits
- If 9 is added to the number, the digits are reversed
To find: The number
Solution:
Let's assume the number to be xy, where x and y are digits.
According to the given information, we have two equations:
1. xy = 5(x+y)
2. xy + 9 = 10y + x
Solving the equations:
From equation 1, we get:
xy = 5x + 5y
xy - 5x = 5y
x(y-5) = 5y
Since x and y are digits, y can't be zero. So, we can divide both sides by y:
x = 5 + 5/y
Since x is a digit, y can only be 1 or 5. But if y is 1, x will be a fraction which is not possible. So, y must be 5.
Putting y=5 in the above equation, we get:
x = 5 + 5/5 = 6
So, the number xy is 65.
Now, from equation 2, we have:
xy + 9 = 10y + x
65 + 9 = 10(5) + 6
74 = 56
But the digits are reversed, so the number must be 47.
Therefore, the correct option is (c) 45.
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Community Answer
A number between 10 and 100 is five times the sum of its digits. If 9 ...
Here rather than solving Go through the options ...
you will notice that only 45 is the no which when added by 9 ... the digits are reversed
therefore the correct ans is option c 45
you will notice that only 45 is the no which when added by 9 ... the digits are reversed
therefore the correct ans is option c 45
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A number between 10 and 100 is five times the sum of its digits. If 9 be added to it the digits are reversed find the number.a)54b)53c)45d)55Correct answer is option 'C'. Can you explain this answer?
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