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The sum of digits of a two digit number is 6. The ratio of the original number to the number formed by interchanging its digits is 4 : 7. Find the number.
- a)60
- b)15
- c)42
- d)33
- e)24
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
The sum of digits of a two digit number is 6. The ratio of the origina...
Let the number is 10x+y
So x+y = 6
And (10x+y)/(10y+x) = 4/7
Solve, 2x = y and from above we have x+y = 6
Solve both equations, x = 2, y = 4
So x+y = 6
And (10x+y)/(10y+x) = 4/7
Solve, 2x = y and from above we have x+y = 6
Solve both equations, x = 2, y = 4
Most Upvoted Answer
The sum of digits of a two digit number is 6. The ratio of the origina...
Let the number is 10x+y
So x+y = 6
And (10x+y)/(10y+x) = 4/7
Solve, 2x = y and from above we have x+y = 6
Solve both equations, x = 2, y = 4
So x+y = 6
And (10x+y)/(10y+x) = 4/7
Solve, 2x = y and from above we have x+y = 6
Solve both equations, x = 2, y = 4
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Community Answer
The sum of digits of a two digit number is 6. The ratio of the origina...
Given,
- Let the two-digit number be represented as AB, where A and B are the digits.
- A + B = 6
- The ratio of the original number to the number formed by interchanging its digits is 4 : 7.
To find: The number represented as AB.
Solution:
Let's represent the original number as 10A + B and the number formed by interchanging its digits as 10B + A.
The ratio of the original number to the number formed by interchanging its digits is 4 : 7.
=> (10A + B) / (10B + A) = 4/7
Simplifying the above equation, we get:
=> 70A + 7B = 40B + 4A
=> 66A = 33B
=> 2A = B
Since A + B = 6, we can substitute B with 2A in the above equation and get:
A + 2A = 6
=> 3A = 6
=> A = 2
and B = 2A = 4
Therefore, the number represented as AB is 24.
Hence, the correct option is (E) 24.
- Let the two-digit number be represented as AB, where A and B are the digits.
- A + B = 6
- The ratio of the original number to the number formed by interchanging its digits is 4 : 7.
To find: The number represented as AB.
Solution:
Let's represent the original number as 10A + B and the number formed by interchanging its digits as 10B + A.
The ratio of the original number to the number formed by interchanging its digits is 4 : 7.
=> (10A + B) / (10B + A) = 4/7
Simplifying the above equation, we get:
=> 70A + 7B = 40B + 4A
=> 66A = 33B
=> 2A = B
Since A + B = 6, we can substitute B with 2A in the above equation and get:
A + 2A = 6
=> 3A = 6
=> A = 2
and B = 2A = 4
Therefore, the number represented as AB is 24.
Hence, the correct option is (E) 24.
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