Problem Based on ages
- The sum of the ages of a daughter and mother is 56 years. After 4 years, the age of the mother will be 3 times that of the daughter. Their respective ages are.
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Suppose the age of mother be P years and that of daughter’s age be Q years.
According to question P + Q = 56 .........(i)
After 4 years, P + 4 = 3 (Q + 4) ⇒ P + 4 = 3Q + 12 ⇒ P – 3Q = 8 ......(ii)Correct Option: B
Suppose the age of mother be P years and that of daughter’s age be Q years.
According to question P + Q = 56 .........(i)
After 4 years, P + 4 = 3 (Q + 4) ⇒ P + 4 = 3Q + 12 ⇒ P – 3Q = 8 ......(ii)
On solving equations (i) and (ii) , we get
Q = 12 years
∴ P = 56 – 12 = 44 years
Hence , the age of mother is 44 years and her daughter’s age is 12 years .
- Ravi is younger to his brother by 3 years. At the time of birth of his sister the age of his father was 28 years and that of his mother was 26 years. The age of his sister was 4 years at the time of birth of his brother. What was the age of his father at the time of the birth of Ravi?
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The age of sister of Ravi at the time of birth of Ravi’s brother = 4 years
Ravi’s sister is 4 + 3 = 7 years elder than Ravi.Correct Option: B
The age of sister of Ravi at the time of birth of Ravi’s brother = 4 years
Ravi’s sister is 4 + 3 = 7 years elder than Ravi.
The age of father at the time of birth of Ravi = 28 + 7 = 35 Years
- At present a father’s age is 30 years more than that of his only son. What was his age when the son was born?
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Suppose the age of son at present = P years
∴ Present age of the father = Present age of son + 30 years
Present age of the father = P + 30 yearsCorrect Option: B
Suppose the age of son at present = P years
∴ Present age of the father = Present age of son + 30 years
Present age of the father = P + 30 years
Age of father at the birth of his son = Present age of the father - Present age of son = ( P + 30 ) – P = 30 years
- 10 years ago, average age of A and B was 20 years. Average age of A, B and C is 30 years today. How old C will be after 5 years?
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Let the present ages of A, B and C be P years, Q years and R years respectively.
According to question,
Ten years ago, average age of A and B = 20 years.(P - 10) + (Q - 10) = 20 2 Correct Option: C
Let the present ages of A, B and C be P years, Q years and R years respectively.
According to question,
Ten years ago, average age of A and B = 20 years.(P - 10) + (Q - 10) = 20 2
⇒ P – 10 + Q – 10 =40
⇒ P + Q = 60 .....(i)
Average present age of A, B and C = 30 yearsAgain, P + Q + R = 30 3
⇒ P + Q + R = 30 × 3 = 90 ....(ii)
On solving equations (i) and (ii) , we get
R = 30 years
Hence, the age of C after 5 years = 30 + 5 = 35 years
- The average age of 19 boys in a class is 21 years. If the teacher’s age is included, the average increases to 22 years. What is the teacher’s age?
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Given that :- The average age of 19 boys in a class = 21 years
Total age of 19 boys = 19 × 21 = 399 years
The average age of 19 boys and teacher = 22 years
Total age of 19 boys and teacher = 20 × 22 = 440 yearsCorrect Option: B
Given that :- The average age of 19 boys in a class = 21 years
Total age of 19 boys = 19 × 21 = 399 years
The average age of 19 boys and teacher = 22 years
Total age of 19 boys and teacher = 20 × 22 = 440 years
∴Teacher’s age = Total age of 19 boys and teacher - Total age of 19 boys
Teacher’s age = 440 – 399 = 41 years
Hence , the age of teacher is 41 years .