Question

7. The ages of two sisters are in the ratio 5:7.
six years later, the sum of their ages will
be 72 years. Find their present ages.​

Answer 1

Answer:

Answer

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Chikuπ

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we have the ratio of two ages ie, 2:3.

So let the common factor of their ages be x.

So their ages are 2x and 3x.

6 years later their ages will be 3:4.

ATQ,

2x+6. 3

____=. _

3x+6. 4

Cross multiplying we get,

3(3x+6)=4(2x+6)

9x+18=8x+24

9x-8x=24-18

x=6,

Hence,

Their present ages will be,

2*6=12

3*6=18

______________________

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Step-by-step explanation:

Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• The ages of two sisters are in the ratio 5 : 7

• Six years later, the sum of their ages will be 72 years.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The present ages of each of them.

$\bf{\underline{\underline\green{Solution:-}}}$

The the common ratio between their ages be x

According to the 1st condition:-

The ages of two sisters are in the ratio 5 : 7

Let the age of first sister be 5x

The age of second sister be 7x

According to the 2nd condition:-

Six years later, the sum of their ages will be 72 years.

After six years:-

Age of first sister = 5x + 6

Age of second sister = 7x + 6

Sum of their ages will be 72 years.

Age of first sister + Age of second sister = 72

→ (5x + 6) + (7x + 6) = 72

→ 5x + 6 + 7x + 6 = 72

→ 12x + 12 = 72

Dividing whole equation by 12

$\rm \rightarrow \dfrac{12x}{12} + \dfrac{12}{12} = \dfrac{72}{12}$

→ x + 1 = 6

→ x = 6 - 1

→ x = 5

Age of first sister

= 5x

= 5 × 5

= 25

Age of second sister

= 7x

= 7 × 5

= 35

Hence;

$\boxed{ \rm Age \: of \: first \: sister = 25 \: years}$

$\boxed{ \rm Age \: of \: second \: sister = 35 \: years}$