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Three years ago, the ratio of ages of Amisha and Namisha was 8:9. Three years from now the ratio will become 11:12. What is the present age of Amisha?

Solution

✅ Correct Option: 3

Let present age of Amisha = xx years

Then present age of Namisha = yy years

Three years ago:

(x−3):(y−3)=8:9(x-3):(y-3) = 8:9

9(x−3)=8(y−3)9(x-3) = 8(y-3) ...(1)

Three years later:

(x+3):(y+3)=11:12(x+3):(y+3) = 11:12

12(x+3)=11(y+3)12(x+3) = 11(y+3) ...(2)

From (1):

9x−27=8y−249x - 27 = 8y - 24

9x−8y=39x - 8y = 3 ...(3)

From (2):

12x+36=11y+3312x + 36 = 11y + 33

12x−11y=−312x - 11y = -3 ...(4)

Subtracting (4) from (3):

−3x+3y=6-3x + 3y = 6

x−y=−2x - y = -2

Substituting in (3):

9x−8(x+2)=39x - 8(x+2) = 3

9x−8x−16=39x - 8x - 16 = 3

x−16=3x - 16 = 3

x=19x = 19

Therefore, Amisha's present age is 19 years.

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