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5 years ago the ratio of the age of A to that of B was 7 : 6. 20 years hence, the ratio of the age of A to that of B will be 22 : 21. What is the sum of their current ages?
- a)30 years
- b)31.67 years
- c)33.33 years
- d)36 years
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
5 years ago the ratio of the age of A to that of B was 7 : 6. 20 years...
Let the age of A 5 years ago = 7x
The age of B 5 years ago = 6x
147x + 525 = 132x + 550
15x = 25
So the answer = (7x + 5 + 6x + 5) = 13x + 10
Hence, Option B is correct.
The age of B 5 years ago = 6x
147x + 525 = 132x + 550
15x = 25
So the answer = (7x + 5 + 6x + 5) = 13x + 10
Hence, Option B is correct.
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Community Answer
5 years ago the ratio of the age of A to that of B was 7 : 6. 20 years...
Given Data:
- 5 years ago, the ratio of A's age to B's age was 7:6.
- 20 years later, the ratio of A's age to B's age will be 22:21.
Let's solve the problem step by step:
Step 1: Set up equations
- Let the current ages of A and B be A and B respectively.
- According to the first statement,
(A-5)/(B-5) = 7/6
- According to the second statement,
(A+20)/(B+20) = 22/21
Step 2: Solve the equations
- Cross multiply the first equation:
6A - 30 = 7B - 35
6A - 7B = -5 ----(i)
- Cross multiply the second equation:
21A + 420 = 22B + 440
21A - 22B = 20 ----(ii)
- Now, solve equations (i) and (ii) simultaneously to find the values of A and B.
Step 3: Find the current ages of A and B
- After solving equations (i) and (ii), we get the current ages of A and B as A=35 and B=30.
Step 4: Find the sum of their current ages
- Sum of their current ages = A + B
= 35 + 30
= 65 years
Therefore, the sum of their current ages is 65 years, which is equivalent to 31.67 years (option b).
- 5 years ago, the ratio of A's age to B's age was 7:6.
- 20 years later, the ratio of A's age to B's age will be 22:21.
Let's solve the problem step by step:
Step 1: Set up equations
- Let the current ages of A and B be A and B respectively.
- According to the first statement,
(A-5)/(B-5) = 7/6
- According to the second statement,
(A+20)/(B+20) = 22/21
Step 2: Solve the equations
- Cross multiply the first equation:
6A - 30 = 7B - 35
6A - 7B = -5 ----(i)
- Cross multiply the second equation:
21A + 420 = 22B + 440
21A - 22B = 20 ----(ii)
- Now, solve equations (i) and (ii) simultaneously to find the values of A and B.
Step 3: Find the current ages of A and B
- After solving equations (i) and (ii), we get the current ages of A and B as A=35 and B=30.
Step 4: Find the sum of their current ages
- Sum of their current ages = A + B
= 35 + 30
= 65 years
Therefore, the sum of their current ages is 65 years, which is equivalent to 31.67 years (option b).
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5 years ago the ratio of the age of A to that of B was 7 : 6. 20 years hence, the ratio of the age of A to that of B will be 22 : 21. What is the sum of their current ages?a)30 yearsb)31.67 yearsc)33.33 yearsd)36 yearsCorrect answer is option 'B'. Can you explain this answer?
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