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Two years ago the ratio of the ages of a mother and her daughter was 8:1. After 2 years the ratio of their ages will be 4:1, Today how many years is the mother elder than her daughter?
Answers
Answer:
21 years
Step-by-step explanation:
Let the present ages of mother be 'x'.
Let the present ages of daughter be 'y'.
(i) Two years ago:
⇒ Age of mother = x - 2
⇒ Age of daughter = y - 2.
Given that 2 years ratio the ages was 8:1
⇒ x - 2 : y - 2 = 8 : 1
⇒ x - 2 = 8(y - 2)
⇒ x - 2 = 8y - 16
⇒ x - 8y = -16 + 2
⇒ x - 8y = -14
(ii) 2 years hence:
⇒ Age of mother = x + 2
⇒ Age of daughter = y + 2
Given that 2 years hence the ratio will be 4:1
⇒ x + 2 : y + 2 = 4 : 1
⇒ x + 2 = 4(y + 2)
⇒ x + 2 = 4y + 8
⇒ x - 4y = 8 - 2
⇒ x - 4y = 6
On solving (i) & (ii), we get
⇒ x - 8y = -14
⇒ x - 4y = 6
-----------------
-4y = -20
y = 5.
Substitute y = 5 in (i), we get
⇒ x - 8y = -14
⇒ x - 8(5) = -14
⇒ x - 40 = -14
⇒ x = 26.
Therefore:
⇒ Present age of mother = 26 years.
⇒ Present age of daughter = 5 years.
Therefore, Mother is 21 years elder than her daughter.
Hope it helps!
Answer:
21
Step-by-step explanation:
present ages of mother be 'x'.
present ages of daughter be 'y'.
Two years ago:
Age of mother = x - 2
Age of daughter = y - 2.
Given that 2 years ratio the ages was 8:1
x - 2 : y - 2 = 8 : 1
x - 2 = 8(y - 2)
x - 2 = 8y - 16
x - 8y = -16 + 2
x - 8y = -14
2 years hence:
Age of mother = x + 2
Age of daughter = y + 2
x + 2 : y + 2 = 4 : 1
x + 2 = 4(y + 2)
x + 2 = 4y + 8
x - 4y = 8 - 2
x - 4y = 6
On solving (i) & (ii), we get
x - 8y = -14
x - 4y = 6
-----------------
-4y = -20
y = 5.
Substitute y = 5 in (i), we get
x - 8y = -14
x - 8(5) = -14
x - 40 = -14
x = 26.
Therefore:
Present age of mother = 26 years.
Present age of daughter = 5 years.
Therefore, Mother is 21 years elder than her daughter.