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Six years ago, Seema was half of that of Rupa in age. Four years hence the respective ratio of their ages would be 3:5. How old is Rupa at present?
- a)32 years
- b)16 years
- c)40 years
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Six years ago, Seema was half of that of Rupa in age. Four years hence...
Let Seema's age at present be x years and Rupa's age be y years,
Now, according to the question,
(y - 6) = 2 (x - 6)
⇒ y - 6 = 2x - 12
or, 2x - y = 6 .....(1)
Also, x + 4/y + 4 = 3/5
or, 5x + 20 = 3y + 12
or, 5x - 3y = -8 .....(2)
From Equations (1) and (2), we get
x = 26 years and y = 46 years
Now, according to the question,
(y - 6) = 2 (x - 6)
⇒ y - 6 = 2x - 12
or, 2x - y = 6 .....(1)
Also, x + 4/y + 4 = 3/5
or, 5x + 20 = 3y + 12
or, 5x - 3y = -8 .....(2)
From Equations (1) and (2), we get
x = 26 years and y = 46 years
Most Upvoted Answer
Six years ago, Seema was half of that of Rupa in age. Four years hence...
Let's assume Seema's present age is S years and Rupa's present age is R years.
Given that six years ago, Seema was half of that of Rupa in age.
So, six years ago, Seema's age = S - 6 years
And six years ago, Rupa's age = R - 6 years
According to the given information, four years hence the respective ratio of their ages would be 3:5.
So, four years from now, Seema's age = S + 4 years
And four years from now, Rupa's age = R + 4 years
According to the given information, the ratio of their ages after four years will be 3:5.
Therefore, we can write the equation as:
(S + 4) / (R + 4) = 3/5
Now, let's solve the equation step by step:
Cross multiplying the equation: 5(S + 4) = 3(R + 4)
5S + 20 = 3R + 12
Rearranging the equation: 5S - 3R = 12 - 20
5S - 3R = -8
Since we have two variables, we need one more equation to solve for their values.
Let's use the information given six years ago:
Seema's age six years ago = half of Rupa's age six years ago
(S - 6) = (1/2)(R - 6)
Simplifying the equation: 2(S - 6) = R - 6
2S - 12 = R - 6
Rearranging the equation: 2S - R = -6 + 12
2S - R = 6
Now, we have a system of two equations:
5S - 3R = -8 ...(Equation 1)
2S - R = 6 ...(Equation 2)
Solving these two equations simultaneously will give us the values of S and R.
Multiplying Equation 2 by 3, we get:
6S - 3R = 18 ...(Equation 3)
Subtracting Equation 3 from Equation 1, we get:
(5S - 3R) - (6S - 3R) = -8 - 18
Simplifying the equation: -S = -26
Dividing by -1 on both sides, we get:
S = 26
Substituting the value of S in Equation 2, we get:
2(26) - R = 6
52 - R = 6
R = 52 - 6
R = 46
Therefore, Rupa's present age is 46 years.
Given that six years ago, Seema was half of that of Rupa in age.
So, six years ago, Seema's age = S - 6 years
And six years ago, Rupa's age = R - 6 years
According to the given information, four years hence the respective ratio of their ages would be 3:5.
So, four years from now, Seema's age = S + 4 years
And four years from now, Rupa's age = R + 4 years
According to the given information, the ratio of their ages after four years will be 3:5.
Therefore, we can write the equation as:
(S + 4) / (R + 4) = 3/5
Now, let's solve the equation step by step:
Cross multiplying the equation: 5(S + 4) = 3(R + 4)
5S + 20 = 3R + 12
Rearranging the equation: 5S - 3R = 12 - 20
5S - 3R = -8
Since we have two variables, we need one more equation to solve for their values.
Let's use the information given six years ago:
Seema's age six years ago = half of Rupa's age six years ago
(S - 6) = (1/2)(R - 6)
Simplifying the equation: 2(S - 6) = R - 6
2S - 12 = R - 6
Rearranging the equation: 2S - R = -6 + 12
2S - R = 6
Now, we have a system of two equations:
5S - 3R = -8 ...(Equation 1)
2S - R = 6 ...(Equation 2)
Solving these two equations simultaneously will give us the values of S and R.
Multiplying Equation 2 by 3, we get:
6S - 3R = 18 ...(Equation 3)
Subtracting Equation 3 from Equation 1, we get:
(5S - 3R) - (6S - 3R) = -8 - 18
Simplifying the equation: -S = -26
Dividing by -1 on both sides, we get:
S = 26
Substituting the value of S in Equation 2, we get:
2(26) - R = 6
52 - R = 6
R = 52 - 6
R = 46
Therefore, Rupa's present age is 46 years.
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Community Answer
Six years ago, Seema was half of that of Rupa in age. Four years hence...
Given that 6 years ago Seema is half of that of Rupa so Ife we take (1/2 ) 2 is Rupa and 1 is Seema (1 is half of 2).
now Seema is 1 and Rupa is 2 ( which is 6 years ago ratio).
it is also given that 4 years aftr their ratio is 3:5(Seema3,rupa5)
before 6 years and aftr 4 years (6+4= 10years).
S. R.
6yrs ago 1. :. 2.
+10yrs. +10yrs
aftr 4 yrs. 3. :. 5. (cross multiply(1*5=5 ,
3*2=6)(6-5=1))
1. :. 20 (cm(5*10=50
3*10=30)(50-30=20))
for 1= 20 then w.r.to given 6yr ago ratio 1:2
for 1= 1*20=20 , for 2 = 2*20=40(6yrs ago ages of Seema and Rupa are 20 and 40 respectively).
present ages ( seema's age is 20+6=26 and Rupa's age is 40+6= 46 years).
aftr 4 years (Seema age 26+4=30 , Rupa age 46+4= 50)(given ratio 3:5).
now Seema is 1 and Rupa is 2 ( which is 6 years ago ratio).
it is also given that 4 years aftr their ratio is 3:5(Seema3,rupa5)
before 6 years and aftr 4 years (6+4= 10years).
S. R.
6yrs ago 1. :. 2.
+10yrs. +10yrs
aftr 4 yrs. 3. :. 5. (cross multiply(1*5=5 ,
3*2=6)(6-5=1))
1. :. 20 (cm(5*10=50
3*10=30)(50-30=20))
for 1= 20 then w.r.to given 6yr ago ratio 1:2
for 1= 1*20=20 , for 2 = 2*20=40(6yrs ago ages of Seema and Rupa are 20 and 40 respectively).
present ages ( seema's age is 20+6=26 and Rupa's age is 40+6= 46 years).
aftr 4 years (Seema age 26+4=30 , Rupa age 46+4= 50)(given ratio 3:5).
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Six years ago, Seema was half of that of Rupa in age. Four years hence the respective ratio of their ages would be 3:5. How old is Rupa at present?a)32 yearsb)16 yearsc)40 yearsd)None of theseCorrect answer is option 'D'. Can you explain this answer?
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Six years ago, Seema was half of that of Rupa in age. Four years hence the respective ratio of their ages would be 3:5. How old is Rupa at present?a)32 yearsb)16 yearsc)40 yearsd)None of theseCorrect answer is option 'D'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Six years ago, Seema was half of that of Rupa in age. Four years hence the respective ratio of their ages would be 3:5. How old is Rupa at present?a)32 yearsb)16 yearsc)40 yearsd)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Six years ago, Seema was half of that of Rupa in age. Four years hence the respective ratio of their ages would be 3:5. How old is Rupa at present?a)32 yearsb)16 yearsc)40 yearsd)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Six years ago, Seema was half of that of Rupa in age. Four years hence the respective ratio of their ages would be 3:5. How old is Rupa at present?a)32 yearsb)16 yearsc)40 yearsd)None of theseCorrect answer is option 'D'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Six years ago, Seema was half of that of Rupa in age. Four years hence the respective ratio of their ages would be 3:5. How old is Rupa at present?a)32 yearsb)16 yearsc)40 yearsd)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Six years ago, Seema was half of that of Rupa in age. Four years hence the respective ratio of their ages would be 3:5. How old is Rupa at present?a)32 yearsb)16 yearsc)40 yearsd)None of theseCorrect answer is option 'D'. Can you explain this answer?.
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Six years ago, Seema was half of that of Rupa in age. Four years hence the respective ratio of their ages would be 3:5. How old is Rupa at present?a)32 yearsb)16 yearsc)40 yearsd)None of theseCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Six years ago, Seema was half of that of Rupa in age. Four years hence the respective ratio of their ages would be 3:5. How old is Rupa at present?a)32 yearsb)16 yearsc)40 yearsd)None of theseCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Six years ago, Seema was half of that of Rupa in age. Four years hence the respective ratio of their ages would be 3:5. How old is Rupa at present?a)32 yearsb)16 yearsc)40 yearsd)None of theseCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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