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The sum of the ages of a Sita’s mother and her daughter is 50 years. Also 5 years ago, the mother’s age was 7 times the age of the daughter. What are the present ages of the mother and the daughter?
- a)45 years,5 years
- b)35 years,15 years
- c)40 years,10 years
- d)42 years,8 years
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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The sum of the ages of a Sita’s mother and her daughter is 50 ye...
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The sum of the ages of a Sita’s mother and her daughter is 50 ye...
Problem Statement
The sum of the ages of Sita's mother and her daughter is 50 years. Five years ago, the mother's age was seven times the daughter's age.
Let’s Define Variables
- Let M = Mother's current age
- Let D = Daughter's current age
Setting Up Equations
1. Age Sum Equation:
M + D = 50
2. Age Relation Equation (5 years ago):
(M - 5) = 7 * (D - 5)
Solving the Equations
- From the first equation, we can express M in terms of D:
M = 50 - D
- Substitute M in the second equation:
(50 - D - 5) = 7 * (D - 5)
This simplifies to:
45 - D = 7D - 35
- Rearranging gives:
45 + 35 = 7D + D
80 = 8D
D = 10
Finding Mother's Age
- Substitute D back into the equation for M:
M = 50 - D
M = 50 - 10 = 40
Final Ages
- Mother's Age: 40 years
- Daughter's Age: 10 years
Conclusion
The present ages of Sita's mother and daughter are 40 years and 10 years, respectively. Therefore, the correct answer is option 'C'.
The sum of the ages of Sita's mother and her daughter is 50 years. Five years ago, the mother's age was seven times the daughter's age.
Let’s Define Variables
- Let M = Mother's current age
- Let D = Daughter's current age
Setting Up Equations
1. Age Sum Equation:
M + D = 50
2. Age Relation Equation (5 years ago):
(M - 5) = 7 * (D - 5)
Solving the Equations
- From the first equation, we can express M in terms of D:
M = 50 - D
- Substitute M in the second equation:
(50 - D - 5) = 7 * (D - 5)
This simplifies to:
45 - D = 7D - 35
- Rearranging gives:
45 + 35 = 7D + D
80 = 8D
D = 10
Finding Mother's Age
- Substitute D back into the equation for M:
M = 50 - D
M = 50 - 10 = 40
Final Ages
- Mother's Age: 40 years
- Daughter's Age: 10 years
Conclusion
The present ages of Sita's mother and daughter are 40 years and 10 years, respectively. Therefore, the correct answer is option 'C'.
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Community Answer
The sum of the ages of a Sita’s mother and her daughter is 50 ye...
Present - > M + D = 50
5 Years Ago - > M' + D' = Sum of ages five years ago(x)
M' = M - 5
D' = D - 5
x = M + D - 5 - 5 = 50-10 = 40
M' = 7*D'
x = 7*D' + D' = 8D' = 40
D' = 5
M' = 40 - 5 = 35
But these are ages 5 years ago.
So,
M = M' + 5 = 40 years
D = D' + 5 = 10 years
5 Years Ago - > M' + D' = Sum of ages five years ago(x)
M' = M - 5
D' = D - 5
x = M + D - 5 - 5 = 50-10 = 40
M' = 7*D'
x = 7*D' + D' = 8D' = 40
D' = 5
M' = 40 - 5 = 35
But these are ages 5 years ago.
So,
M = M' + 5 = 40 years
D = D' + 5 = 10 years
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The sum of the ages of a Sita’s mother and her daughter is 50 years. Also 5 years ago, the mother’s age was 7 times the age of the daughter. What are the present ages of the mother and the daughter?a)45 years,5 yearsb)35 years,15 yearsc)40 years,10 yearsd)42 years,8 yearse)None of theseCorrect answer is option 'C'. Can you explain this answer?
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