3) 4 years ago, Swapna's mother was 3 times as old as
Swapna. After 6 years she will be twice as old as Swapna.
Present age (in years) of Swapna's mother is
A) 39
B) 36
C) 34
D) 24
Answers
ANSWER :-
- Option C , 34
GIVEN :-
- 4 years ago , Swapna's mother was 3 times as old as Swapna.
- After 6 years , Swapna's mother will be twice as old as Swapna.
TO FIND :-
- Present age of Swapna's mother.
SOLUTION :-
Let age of Swapna be 'x' and age of Swapna's mother be 'y'.
According to question ,
♦ 4 years ago, Swapna's mother was 3 times as old as Swapna.
4 years ago ,
- Age of Swapna = x - 4
- Age of Swapna's mother = y - 4
So,
→ y - 4 = 3(x - 4)
→ y - 4 = 3x - 12
→ y - 3x = - 12 + 4
→ y - 3x = - 8 ---------(i)
____________________
♦ Also , after 6 years, Swapna's mother will be twice as old as Swapna.
6 years later ,
- Age of Swapna's mother = y + 6
- Age of Swapna = x + 6
So,
→ y + 6 = 2(x + 6)
→ y + 6 = 2x + 12
→ y - 2x = 12 - 6
→ y - 2x = 6 ----------(ii)
Subtracting equation (ii) by equation (i),
→ y - 3x - (y - 2x) = - 8 - 6
→ y - 3x - y + 2x = -14
→ -x = -14
→ x = 14 years
Hence , age of Swapna is 14years.
____________________
Putting value of 'x' in equation (ii) ,
→ y - 2x = 6
→ y - 2(14) = 6
→ y - 28 = 6
→ y = 34 years
Hence , age of Swapna's mother is 34 years. Option C.
Answer:
c) 34 years
Solution:
Let Present ages of
- Swapnas mother be m
- Swapna be s
4 years ago,
- Swapna's mother's age = (m - 4)
- Swapna's age = (s - 4)
According to the question,
(m - 4) = 3(s - 4)
⇒ m - 4 = 3s - 12
⇒ m - 4 + 12 = 3s
⇒ m + 8 = 3s -------- [Equation 1]
After 6 years,
- Swapna's mother's age = (m + 6)
- Swapna's age = (s + 6)
According to the question,
(m + 6) = 2(s + 6)
⇒ m + 6 = 2s + 12
⇒ m = 2s + 12 - 6
⇒ m = 2s + 6 ------- [Equation 2]
Substitute the value of m from Equation 2 in Equation 1
m + 8 = 3s
⇒ (2s + 6) + 8 = 3s
⇒ 2s + 6 + 8 = 3s
⇒ 2s + 14 = 3s
⇒ 3s - 2s = 14
∴ s = 14
Now, substitute the value of s in Equation 1 to get the value of m
m = 2s + 6
→ m = 2(14) + 6
→ m = 28 + 6