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If 1/3rd of the first of the three consecutive odd numbers is 2 more than 1/5th of the third number, then the second number is?
- a)21
- b)23
- c)25
- d)19
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If 1/3rdof the first of the three consecutive odd numbers is 2 more th...
To solve this problem, let's assume the first odd number as x.
First Odd Number: x
Second Odd Number: x + 2 (since the numbers are consecutive odd numbers)
Third Odd Number: x + 4 (since the numbers are consecutive odd numbers)
According to the given information:
1/3rd of the first number is 2 more than 1/5th of the third number.
Mathematically, this can be represented as:
1/3 * x = (1/5 * (x + 4)) + 2
Now, let's solve this equation step by step.
Step 1: Simplify the equation
1/3 * x = 1/5 * (x + 4) + 2
Step 2: Multiply both sides of the equation by the least common multiple (LCM) of 3 and 5, which is 15, to eliminate the fractions.
15 * (1/3 * x) = 15 * (1/5 * (x + 4) + 2)
5x = 3(x + 4) + 30
Step 3: Distribute on the right side of the equation
5x = 3x + 12 + 30
Step 4: Combine like terms
5x = 3x + 42
Step 5: Subtract 3x from both sides of the equation
5x - 3x = 42
2x = 42
Step 6: Divide both sides of the equation by 2
x = 42/2
x = 21
Now that we have the value of x, we can find the second number by adding 2 to the first number.
Second Odd Number = x + 2 = 21 + 2 = 23
Therefore, the second number is 23, which matches with option B.
First Odd Number: x
Second Odd Number: x + 2 (since the numbers are consecutive odd numbers)
Third Odd Number: x + 4 (since the numbers are consecutive odd numbers)
According to the given information:
1/3rd of the first number is 2 more than 1/5th of the third number.
Mathematically, this can be represented as:
1/3 * x = (1/5 * (x + 4)) + 2
Now, let's solve this equation step by step.
Step 1: Simplify the equation
1/3 * x = 1/5 * (x + 4) + 2
Step 2: Multiply both sides of the equation by the least common multiple (LCM) of 3 and 5, which is 15, to eliminate the fractions.
15 * (1/3 * x) = 15 * (1/5 * (x + 4) + 2)
5x = 3(x + 4) + 30
Step 3: Distribute on the right side of the equation
5x = 3x + 12 + 30
Step 4: Combine like terms
5x = 3x + 42
Step 5: Subtract 3x from both sides of the equation
5x - 3x = 42
2x = 42
Step 6: Divide both sides of the equation by 2
x = 42/2
x = 21
Now that we have the value of x, we can find the second number by adding 2 to the first number.
Second Odd Number = x + 2 = 21 + 2 = 23
Therefore, the second number is 23, which matches with option B.
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Community Answer
If 1/3rdof the first of the three consecutive odd numbers is 2 more th...
Given:
1/3rd of the first of the three consecutive odd numbers is 2 more than 1/5th of the third number.
Calculation:
Let, the three consecutive odd numbers be x, x + 2 and x + 4 respectively, then
According to the question,
x × (1/3) = (x + 4) × (1/5) + 2
⇒ x/3 = (x + 4 + 10)/5
⇒ 5x = 3x + 42
⇒ 5x – 3x = 42
⇒ 2x = 42
⇒ x = 21
∴ Second odd number is x + 2 = 21 + 2 = 23
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