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Two numbers are in the ratio of 5:8 .If 4 is subtracted from each then the ratio become 1:2.The small number is
- a)16
- b)4
- c)10
- d)2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two numbers are in the ratio of 5:8 .If 4 is subtracted from each then...
C)10
Explanation : 5x-4/8x-4 = ½ 10x-8 = 8x-4 2x = 4 X=2
5(2) = 10
Explanation : 5x-4/8x-4 = ½ 10x-8 = 8x-4 2x = 4 X=2
5(2) = 10
Most Upvoted Answer
Two numbers are in the ratio of 5:8 .If 4 is subtracted from each then...
Question:
Two numbers are in the ratio of 5:8. If 4 is subtracted from each, then the ratio becomes 1:2. Find the smaller number.
Solution:
Let's assume the two numbers in the ratio 5:8 to be 5x and 8x, where x is a common factor.
Step 1: Formulating the first equation:
According to the given information, the ratio of the two numbers is 5:8.
So, we can write the equation as:
5x/8x = 5/8
Step 2: Simplifying the first equation:
Cross-multiplying, we get:
(5x * 8) = (8x * 5)
40x = 40x
This equation shows that the two numbers are in proportion.
Step 3: Formulating the second equation:
According to the given information, if 4 is subtracted from each number, the ratio becomes 1:2.
So, after subtracting 4, the new numbers are (5x - 4) and (8x - 4).
Writing the equation using the new numbers:
(5x - 4)/(8x - 4) = 1/2
Step 4: Simplifying the second equation:
Cross-multiplying, we get:
(5x - 4) * 2 = (8x - 4) * 1
10x - 8 = 8x - 4
10x - 8x = -4 + 8
2x = 4
x = 4/2
x = 2
Step 5: Finding the smaller number:
We need to find the smaller number from the ratio 5:8.
Substituting the value of x in 5x, we get:
Smaller number = 5 * 2 = 10
Therefore, the smaller number is 10.
Hence, option C is the correct answer.
Two numbers are in the ratio of 5:8. If 4 is subtracted from each, then the ratio becomes 1:2. Find the smaller number.
Solution:
Let's assume the two numbers in the ratio 5:8 to be 5x and 8x, where x is a common factor.
Step 1: Formulating the first equation:
According to the given information, the ratio of the two numbers is 5:8.
So, we can write the equation as:
5x/8x = 5/8
Step 2: Simplifying the first equation:
Cross-multiplying, we get:
(5x * 8) = (8x * 5)
40x = 40x
This equation shows that the two numbers are in proportion.
Step 3: Formulating the second equation:
According to the given information, if 4 is subtracted from each number, the ratio becomes 1:2.
So, after subtracting 4, the new numbers are (5x - 4) and (8x - 4).
Writing the equation using the new numbers:
(5x - 4)/(8x - 4) = 1/2
Step 4: Simplifying the second equation:
Cross-multiplying, we get:
(5x - 4) * 2 = (8x - 4) * 1
10x - 8 = 8x - 4
10x - 8x = -4 + 8
2x = 4
x = 4/2
x = 2
Step 5: Finding the smaller number:
We need to find the smaller number from the ratio 5:8.
Substituting the value of x in 5x, we get:
Smaller number = 5 * 2 = 10
Therefore, the smaller number is 10.
Hence, option C is the correct answer.
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Community Answer
Two numbers are in the ratio of 5:8 .If 4 is subtracted from each then...
C)10
Explanation : 5x-4/8x-4 = ½ 10x-8 = 8x-4 2x = 4 X=2
5(2) = 10
Explanation : 5x-4/8x-4 = ½ 10x-8 = 8x-4 2x = 4 X=2
5(2) = 10
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Two numbers are in the ratio of 5:8 .If 4 is subtracted from each then the ratio become 1:2.The small number isa)16b)4c)10d)2Correct answer is option 'C'. Can you explain this answer?
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