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The age of the two friends were in the ratio of 2:3.If the sum of their ages is 55.Then after how many years their ratio will become 4:5?
- a)11
- b)22
- c)33
- d)44
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The age of the two friends were in the ratio of 2:3.If the sum of thei...
Let the age be the friends be 2x and 3x. Sum of their ages = 55
2x + 3x = 55 => 5x=55 => x=11
Their ages are 22 and 33
After k years both of them will be 22+k and 33+k years old
Ratio of their age at that time will me 4:5
- (22+k)/(33+k)=4/5
- 5(22+k)=4(33+4) => 110 + 5k = 132+4k
- K=132-110 = 22
Most Upvoted Answer
The age of the two friends were in the ratio of 2:3.If the sum of thei...
Given:
The age of the two friends is in the ratio of 2:3.
The sum of their ages is 55.
Let's assume the ages of the two friends are 2x and 3x respectively.
Step 1: Calculate the current ages of the two friends:
According to the given ratio, 2x + 3x = 55.
Simplifying the equation, we get 5x = 55.
Dividing both sides by 5, we get x = 11.
Therefore, the current ages of the two friends are:
Friend 1: 2x = 2 * 11 = 22 years
Friend 2: 3x = 3 * 11 = 33 years
Step 2: Determine the number of years required for the ratio to become 4:5:
Let's assume the number of years required is 'y'.
After 'y' years, the ages of the two friends will be:
Friend 1: 22 + y
Friend 2: 33 + y
The new ratio of their ages will be:
(22 + y):(33 + y) = 4:5
Cross-multiplying, we get:
5(22 + y) = 4(33 + y)
110 + 5y = 132 + 4y
5y - 4y = 132 - 110
y = 22
Therefore, after 22 years, the ratio of their ages will become 4:5.
Hence, the correct answer is option B) 22.
The age of the two friends is in the ratio of 2:3.
The sum of their ages is 55.
Let's assume the ages of the two friends are 2x and 3x respectively.
Step 1: Calculate the current ages of the two friends:
According to the given ratio, 2x + 3x = 55.
Simplifying the equation, we get 5x = 55.
Dividing both sides by 5, we get x = 11.
Therefore, the current ages of the two friends are:
Friend 1: 2x = 2 * 11 = 22 years
Friend 2: 3x = 3 * 11 = 33 years
Step 2: Determine the number of years required for the ratio to become 4:5:
Let's assume the number of years required is 'y'.
After 'y' years, the ages of the two friends will be:
Friend 1: 22 + y
Friend 2: 33 + y
The new ratio of their ages will be:
(22 + y):(33 + y) = 4:5
Cross-multiplying, we get:
5(22 + y) = 4(33 + y)
110 + 5y = 132 + 4y
5y - 4y = 132 - 110
y = 22
Therefore, after 22 years, the ratio of their ages will become 4:5.
Hence, the correct answer is option B) 22.
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