Let Maya’s present age be M and Sikhas present age be S.
3 years ago, the ratio of Maya’s and Shika’s age was 5 : 9 respectively.
According to question:
S−;3M−;3 =
95
⇒ 9(M – 3) = 5(S – 3)
⇒ 9M – 27 = 5S – 15
⇒ 9M – 5S = 27 – 15
⇒ 9M – 5S = 12
⇒ 59M−;12= S ----(i)
After 5 years, this ratio would become 3 : 5.
According to question:
S;+;5M;+;5 =
53
⇒ 5(M + 5) = 3(S + 5)
⇒ 5M + 25 = 3S + 15
⇒ 5M – 3S = - 10 ----(ii)
Substituting the value of (i) in (ii), we get:
⇒ 5M - 53;(9M−;12) = - 10
⇒ 25M – 27M + 36 = - 50
⇒ - 2M = - 50 – 36
⇒ - 2M = - 86
⇒ M = 43
Hence, the present age of Maya is ‘43’ years.
Additional InformationLet's suppose, present age of Maya and Shikha is X and Y.
First we balance out the difference of numerator and denominator of the Ratio separately.
So, there difference of 4 in the ratio before 3 years age and difference of 2 between the ratio of age after 5 years. To balance out this, multiply by 2 in the numerator and denominator of ratio after 5 years.
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Now, there is 8 years difference in between the age before 3 years and after 5 years.
In the numerator and denominator of both the ratios, there should also be difference of 8, but there is difference of 1.
So, to balance out this, multiply by 8 in numerator of denominator of both the ratios.
⇒
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⇒
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Now, either add 3 in the numerator and denominator of ratio of the age before 3 years or subtract 5 from numerator and denominator of ratio of the age after 5 years, to get the present age.
⇒
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Hence, we have present age of Maya is 43.