Ratio

Number Theory Level 2

10 years ago, the ratio of daughter and mother was 1:7. After 10 years, the ratio of the ages would be 1:2. Find the present age of daughter.


The answer is 14.

Anuj Shikarkhane by Anuj Shikarkhane , 19, India

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3 solutions

(x-10)/(y-10)=1/7

(x+10)/(y+10)=1/2

Then 2(x+10)-10=7(x-10)+10

So

5x=70

x=14

1 Helpful 0 Interesting 0 Brilliant 0 Confused

this is wrong. According to the question, it's not expected this result. The phrase is better understood as ten years ago .. and 10 years after ten years ago, that is, now. And then, the answer would be 2

Humberto Bento - 6 years, 10 months ago
汶良 林
Jul 28, 2015

10 years ago, daughter : mother = 1 : 7

10 years after, daughter : mother = 1 : 2

7 - 1 = 6, 2 - 1 = 1

Since the difference of their ages never change,

10 years ago, daughter : mother = 1 : 7

10 years after, daughter : mother = 1×6 : 2×6 = 6 : 12

6 - 1 = 12 - 7 = 5

but the difference of ages should be 20, so

10 years ago, daughter : mother = 1×4 : 7×4 = 4 : 28

10 years after, daughter : mother = 6×4 : 12×4 = 24 : 48

24 - 4 = 48 - 28 = 20

10 years ago, daughter's age = 4, mother's age = 28

10 years after, daughter's age = 24, mother's age = 48

Therefore, the present age of the daughter is 4 + 10 = 14.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Consider the present ages of daughter and mother as X and Y respectively.

then subtract 10 from both for before 10 year expression i.e.

(X-10)/(Y-10) = 1/7

add 10 in both for after 10 year expression so

(X+10)/(Y+10) = 1/2

then simplifying these two expressions we get,

7X - Y = 60 and 2X - Y = -10

after subtracting the second equation from the first and you'll get the answer

X = 14 and Y = 38 (both the values show present age).

0 Helpful 0 Interesting 0 Brilliant 0 Confused

This is wrong. Ten years ago the ages where 1/7, so after 10 years which is today, the ages are 1/2. So present day ages are daughter 12 and mother 24 .

Giorgio Coniglio - 6 years, 9 months ago

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