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The ratio of a two-digit natural number to a number formed by reversing its digits is 4: 7. Which of the following is the sum of all the numbers of all such pairs?
- a)99
- b)198
- c)330
- d)32
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The ratio of a two-digit natural number to a number formed by reversin...
Let the two digit natural number be 10x + y.
On reversing = 10y + x.
Therefore 10x+y : 10y+x = 4:7
=> x:y = 1:2
Such numbers are 12,21,24,42,36,63,48,84. Their sum is 330.
Directions (6-8)
On reversing = 10y + x.
Therefore 10x+y : 10y+x = 4:7
=> x:y = 1:2
Such numbers are 12,21,24,42,36,63,48,84. Their sum is 330.
Directions (6-8)
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Community Answer
The ratio of a two-digit natural number to a number formed by reversin...
Understanding the problem:
The problem states that the ratio of a two-digit number to the number formed by reversing its digits is 4:7.
Let's assume:
Let the number be 10x + y, where x is the tens digit and y is the units digit.
The number formed by reversing its digits would be 10y + x.
Setting up the equation:
According to the given ratio, we can write:
(10x + y) / (10y + x) = 4/7
Cross multiplying, we get:
7(10x + y) = 4(10y + x)
70x + 7y = 40y + 4x
70x - 4x = 40y - 7y
66x = 33y
x/y = 33/66 = 1/2
Listing down the pairs:
The possible pairs of numbers would be:
12 & 21 (1/2)
24 & 42 (1/2)
36 & 63 (1/2)
48 & 84 (1/2)
60 & 06 (Invalid as a two-digit number cannot start with 0)
72 & 27 (1/2)
84 & 48 (1/2)
96 & 69 (1/2)
Calculating the sum:
Adding all the pairs, we get:
12 + 21 + 24 + 42 + 36 + 63 + 48 + 84 + 72 + 27 + 84 + 48 + 96 + 69 = 330
Therefore, the sum of all such pairs is 330, which corresponds to option 'C'.
The problem states that the ratio of a two-digit number to the number formed by reversing its digits is 4:7.
Let's assume:
Let the number be 10x + y, where x is the tens digit and y is the units digit.
The number formed by reversing its digits would be 10y + x.
Setting up the equation:
According to the given ratio, we can write:
(10x + y) / (10y + x) = 4/7
Cross multiplying, we get:
7(10x + y) = 4(10y + x)
70x + 7y = 40y + 4x
70x - 4x = 40y - 7y
66x = 33y
x/y = 33/66 = 1/2
Listing down the pairs:
The possible pairs of numbers would be:
12 & 21 (1/2)
24 & 42 (1/2)
36 & 63 (1/2)
48 & 84 (1/2)
60 & 06 (Invalid as a two-digit number cannot start with 0)
72 & 27 (1/2)
84 & 48 (1/2)
96 & 69 (1/2)
Calculating the sum:
Adding all the pairs, we get:
12 + 21 + 24 + 42 + 36 + 63 + 48 + 84 + 72 + 27 + 84 + 48 + 96 + 69 = 330
Therefore, the sum of all such pairs is 330, which corresponds to option 'C'.
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The ratio of a two-digit natural number to a number formed by reversing its digits is 4: 7. Which of the following is the sum of all the numbers of all such pairs?a)99b)198c)330d)32Correct answer is option 'C'. Can you explain this answer?
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