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6 years ago, A was half as old as C and presently he is 2/3 times as old as B. 6 years from now, the ratio of the age of B to that of C will be 15 : 16. What is the present age (in years) of B?
- a)30
- b)32
- c)24
- d)36
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
6 years ago, A was half as old as C and presently he is 2/3 times as o...
3x + 15 : 4x + 12 = 15 : 16
x = 5
Present age of B = 3x + 9 = 3 × 5 + 9 = 24 years
Hence, Option C is correct.
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Community Answer
6 years ago, A was half as old as C and presently he is 2/3 times as o...
Let's break down the problem step by step:
Step 1: Set up equations using the given information.
- Let's assume the present age of A, B, and C as A, B, and C respectively.
- 6 years ago, A was half as old as C, so we can write the equation: A - 6 = (C - 6)/2.
- Presently, A is 2/3 times as old as B, so we can write the equation: A = (2/3)B.
- 6 years from now, the ratio of the age of B to that of C will be 15:16, so we can write the equation: (B + 6)/(C + 6) = 15/16.
Step 2: Solve the equations simultaneously.
- Let's solve the equations to find the values of A, B, and C.
- From the equation A = (2/3)B, we can substitute this value into the equation A - 6 = (C - 6)/2:
(2/3)B - 6 = (C - 6)/2.
Multiplying both sides by 6 to eliminate the fractions, we get:
4B - 36 = 3C - 18.
Rearranging the equation, we have:
4B - 3C = 18.
- Now, let's substitute the value of A in the equation (B + 6)/(C + 6) = 15/16:
(2/3)B + 6 = (15/16)(C + 6).
Multiplying both sides by 16 to eliminate the fractions, we get:
10B + 96 = 15C + 90.
Rearranging the equation, we have:
10B - 15C = -6.
- Now we have a system of equations:
4B - 3C = 18,
10B - 15C = -6.
Solving these equations simultaneously, we find B = 24 and C = 32.
Step 3: Determine the present age of B.
- We found that B = 24, so the present age of B is 24 years.
Therefore, the correct answer is option C) 24.
Step 1: Set up equations using the given information.
- Let's assume the present age of A, B, and C as A, B, and C respectively.
- 6 years ago, A was half as old as C, so we can write the equation: A - 6 = (C - 6)/2.
- Presently, A is 2/3 times as old as B, so we can write the equation: A = (2/3)B.
- 6 years from now, the ratio of the age of B to that of C will be 15:16, so we can write the equation: (B + 6)/(C + 6) = 15/16.
Step 2: Solve the equations simultaneously.
- Let's solve the equations to find the values of A, B, and C.
- From the equation A = (2/3)B, we can substitute this value into the equation A - 6 = (C - 6)/2:
(2/3)B - 6 = (C - 6)/2.
Multiplying both sides by 6 to eliminate the fractions, we get:
4B - 36 = 3C - 18.
Rearranging the equation, we have:
4B - 3C = 18.
- Now, let's substitute the value of A in the equation (B + 6)/(C + 6) = 15/16:
(2/3)B + 6 = (15/16)(C + 6).
Multiplying both sides by 16 to eliminate the fractions, we get:
10B + 96 = 15C + 90.
Rearranging the equation, we have:
10B - 15C = -6.
- Now we have a system of equations:
4B - 3C = 18,
10B - 15C = -6.
Solving these equations simultaneously, we find B = 24 and C = 32.
Step 3: Determine the present age of B.
- We found that B = 24, so the present age of B is 24 years.
Therefore, the correct answer is option C) 24.
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6 years ago, A was half as old as C and presently he is 2/3 times as old as B. 6 years from now, the ratio of the age of B to that of C will be 15 : 16. What is the present age (in years) of B?a)30b)32c)24d)36Correct answer is option 'C'. Can you explain this answer?
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6 years ago, A was half as old as C and presently he is 2/3 times as old as B. 6 years from now, the ratio of the age of B to that of C will be 15 : 16. What is the present age (in years) of B?a)30b)32c)24d)36Correct answer is option 'C'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about 6 years ago, A was half as old as C and presently he is 2/3 times as old as B. 6 years from now, the ratio of the age of B to that of C will be 15 : 16. What is the present age (in years) of B?a)30b)32c)24d)36Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 6 years ago, A was half as old as C and presently he is 2/3 times as old as B. 6 years from now, the ratio of the age of B to that of C will be 15 : 16. What is the present age (in years) of B?a)30b)32c)24d)36Correct answer is option 'C'. Can you explain this answer?.
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