Question

the ages of 2 girls are in the ratio 3:2. 5 years from now their age will be 4:3. find their present age

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Answer 1

Answer:

15 years and 10 years

Step-by-step explanation:

Let common multiple be x

Present age = 3x yrs and 2x yrs

5 years from now

Let common multiple be y

3x + 5 = 4y

3x - 4y = -5......(1)

2x + 5 = 3y

2x - 3y = -5........(2)

LCM OF 2 & 3 = 6

Multiplying (1) by 2 and (2) by 3, we get

6x - 8y = -10......(3)

6x - 9y = -15......(4)

Subtracting (4) from (3)

     6x - 8y = -10

  -  6x - 9y = -15

      -    +       +

             y   = 5

Substituting y = 5 in (2)

2x - 3(5) = -5

2x - 15 = -5

2x = -5 + 15

2x = 10

x = 5

Present age = 15 yrs and 10 years

Answer 2

Answer:

$</p><p> \sf \huge \underline\red{Given:} \\ \\ \sf \: Ratio \: of \: the \: two \: girls. \\ \\ \sf \: Ratio \: after \: 5 \: years. \: \\ \\ \sf \huge \underline \green{To \: Find:} \\ \\ \sf \: Their \:present \: ages. \\ \\ \sf \huge \underline \pink{Solution:} \\ \\ \sf let \: the \: present \: age \: of \: first \: girl \: be \: 3x \\ \\ \sf\:then \: the \: present \: age \: of \: other \: girl = 2x \\ \\ \sf \: After \: 5 \: years, \\ \\ \sf \: First \: girl \: age \: will \: be \: 3x + 5 \: years \\ \\ \sf Other \: girl \: age \: will \: be =2x + 5 \: years \\ \\ \sf \: ACQ, \\ \\ \sf \: \frac{3x + 5}{2x+ 5} = \frac{4}{3} \\ \\ \sf \: 3(3x + 5) = 4(2x + 5) \: [Cross Multiplication] \\ \\ \sf 9x + 15 = 8x + 20 \\ \\ \sf 9x - 8x = 20 - 15 \\ \\ \sf x = 5 \\ \\ \sf Present \: age \: of \: first \: girl = 3 \times 5 = 15 \: years \\ \\ \sf \: Present \: age \: of \: other \: girl = 2 \times 5 = 10 \: years$