Question

If the ratio of the present age of A and B is 5 ratio 7 and after 4 years the ratio of their ages will be 3 ratio 4 then find their present age.

Answer 1

Ratio of Present age of A and B=5:7

Let Present Age of A=5x years

Let Present Age of B=7x years

After 4 years

Age of A will be=(5x+4) years

Age of B will be=(7x+4) years

Now Ratio of Their Age will be after 4 years.=3:4

Ratio a:b can be written as a/b

So.

Age Of A after 4 years:Age of B after 4 years=3:4

5x+4:7x+4=3:4

$\frac{5x + 4}{7x + 4} = \frac{3}{4} \\ \\ 4(5x + 4) = 3(7x + 4) \\ \\ 20x + 16 = 21x + 12 \\ \\ 20x - 21x = 12 - 16 \\ \\ - x = - 4 \\ \\ x = 4$

Age of A=5x=5×4=20 years

Age of B=7x=7×4=28 years

Explanation.

You are now Thinking Why We Assume Ratio as 5x and 7x years or Age.

Or You thinking Why We Assume x with Ratio.

Let 90 and 100 are in Ratio.

90:100

It can Written as=90/100

=9/10

How 9/10 come by Dividing it with HCF 10.

So We take X as HCF So when We Multiply with Ratio Given.It gives Right age.

A's Age=20 years

B's Age=28 years

Answer 2

» According to question

Ratio of Present age of A and B = 5:7

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• Let Present age of A be 5x years

• Let Present age of B be 7x years

» After 4 years

Age of A will = (5x+4) years

Age of B will = (7x+4) years

=============================

» Now

Ratio of their age after 4 years = 3:4

Age of A after 4 years:Age of B after 4 years = 3:4

=> 5x + 4 : 7x + 4 = 3:4

=> $\dfrac{5x \: + \: 4}{7x \: + \: 4}$ = $\dfrac{3}{4}$

» Cross-multiply them

=> 4(5x + 4) = 3(7x + 4)

=> 20x + 16 = 21x + 12

=> 20x - 21x = 12 - 16

=> - x = - 4

=> x = 4

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Present age of A = 5x = 5 × 4 = 20 years

Present age of B = 7x = 7 × 4 = 28 years

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