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The ratio between a two-digit number and the sum of the digits of that number is 4 : 1. If the digit in the unit's is three more than the digit in the ten's places, what is the number?
- a)25
- b)36
- c)47
- d)58
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The ratio between a two-digit number and the sum of the digits of tha...
Let the ten's digit be x. then, unit's digit = (x + 3).
Sum of the digits = x + (x + 3) = 2x + 3.
Let the number = 10x + (x +3) = 11x + 3
So, (11x+3)/(2x+3) = 4/1
⇒ 11x + 3 = 4(2x + 3) ⇔ 11x + 3 = 4 (2x + 3)
⇒ 3x = 9 ⇒ x = 3
Hence, required number = 11x + 3 ⇒ 36.
Hence, option B is correct.
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Community Answer
The ratio between a two-digit number and the sum of the digits of tha...
To solve this problem, we need to find a two-digit number that satisfies the given conditions. Let's break down the information provided step by step:
1. The ratio between a two-digit number and the sum of its digits is 4:1. Let's represent the tens digit as x and the units digit as (x + 3) since the units digit is three more than the tens digit.
2. The sum of the digits is (x + (x + 3)) = 2x + 3.
3. According to the given condition, the ratio between the number (10x + (x + 3)) and the sum of its digits (2x + 3) is 4:1. This can be expressed as:
(10x + (x + 3))/(2x + 3) = 4/1.
4. Simplifying the equation, we get:
10x + x + 3 = 8x + 12.
5. Combining like terms, we have:
11x + 3 = 8x + 12.
6. Subtracting 8x from both sides, we get:
3x + 3 = 12.
7. Subtracting 3 from both sides, we have:
3x = 9.
8. Dividing both sides by 3, we find:
x = 3.
9. Therefore, the tens digit is 3, and the units digit is (3 + 3) = 6.
10. The two-digit number is 36.
Hence, the correct answer is option B) 36.
1. The ratio between a two-digit number and the sum of its digits is 4:1. Let's represent the tens digit as x and the units digit as (x + 3) since the units digit is three more than the tens digit.
2. The sum of the digits is (x + (x + 3)) = 2x + 3.
3. According to the given condition, the ratio between the number (10x + (x + 3)) and the sum of its digits (2x + 3) is 4:1. This can be expressed as:
(10x + (x + 3))/(2x + 3) = 4/1.
4. Simplifying the equation, we get:
10x + x + 3 = 8x + 12.
5. Combining like terms, we have:
11x + 3 = 8x + 12.
6. Subtracting 8x from both sides, we get:
3x + 3 = 12.
7. Subtracting 3 from both sides, we have:
3x = 9.
8. Dividing both sides by 3, we find:
x = 3.
9. Therefore, the tens digit is 3, and the units digit is (3 + 3) = 6.
10. The two-digit number is 36.
Hence, the correct answer is option B) 36.
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The ratio between a two-digit number and the sum of the digits of that number is 4 : 1. If the digit in the unit's is three more than the digit in the ten's places, what is the number?a)25b)36c)47d)58Correct answer is option 'B'. Can you explain this answer?
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