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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 it, the digits are reversed
To find: The number
Solution:
Let the number be represented by 10a + b, where a and b are the tens and units digits respectively.
According to the given information, we have two equations:
- 10a + b = 5(a + b)
- 10a + b + 9 = 10b + a
Simplifying these equations, we get:
- 5a = 4b
- 9a - 9b = 9
From the first equation, we can see that b must be a multiple of 5. The only possible values for b are 5 and 0. However, b cannot be 0 as the number must be between 10 and 100.
Therefore, b = 5 and a = 4. Substituting these values in the second equation, we get:
- 36 = 10b - 9a
- 36 = 10(5) - 9(4)
- 36 = 50 - 36
So, the number is 45.
Therefore, option (c) is the correct answer.
- A number between 10 and 100
- The number is five times the sum of its digits
- If 9 is added to it, the digits are reversed
To find: The number
Solution:
Let the number be represented by 10a + b, where a and b are the tens and units digits respectively.
According to the given information, we have two equations:
- 10a + b = 5(a + b)
- 10a + b + 9 = 10b + a
Simplifying these equations, we get:
- 5a = 4b
- 9a - 9b = 9
From the first equation, we can see that b must be a multiple of 5. The only possible values for b are 5 and 0. However, b cannot be 0 as the number must be between 10 and 100.
Therefore, b = 5 and a = 4. Substituting these values in the second equation, we get:
- 36 = 10b - 9a
- 36 = 10(5) - 9(4)
- 36 = 50 - 36
So, the number is 45.
Therefore, option (c) is the correct answer.
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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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