Question

The ratio of sara's age 4 years ago and vaishali's age after 4 years is 1: 1. Presently, the ratio of their ages is 5: 3. Find the ratio between sara's age 4 years hence and vaishali's age 4 years ago.

Answer 1

Step-by-step explanation:

Let present age of Sara be s and Vaishali v, then

$\frac{s - 4}{v + 4} = \frac{1}{1} \\ \\ s - 4 = v + 4 \\ s - v = 8 \: .......(1)$

presently,

$\frac{s}{v} = \frac{5}{3} \\ \\ 3s - 5v = 0 \: ........(2)$

on solving both equation 1 and 2

s=20 , v= 12

therefore ,

required ratio =

$\frac{20 + 4}{12 - 4} = \frac{3}{1}$

Answer 2

The ratio between Sara's age  4 years hence and Vaishali's age 4 years ago is 7:1  .

Explanation:

Given : The ratio of the present ages of Sara and Vaishali is 5: 3.

Let Present age of Sara = 5x

Present age of Vaishali  = 3x

Sara's age 4 years ago  = 5x-4

Vaishali's age after 4 years = 3x+4

The ratio of Sara's age 4 years ago and Vaishali's age after 4 years will be :

$\dfrac{5x-4}{3x+4}=\dfrac{1}{1}\\\\ 5x-4=3x+4\\\\ 5x-3x=4+4\\\\ 2x=8\\\\ x=2$

∴ Present age of Sara = 5(2) = 10 years

Present age of Vaishali  = 3(2) = 6 years

⇒ Sara's age  4 years hence = 10+4=14  years

Vaishali's age 4 years ago =6-4=2

⇒  The ratio between Sara's age  4 years hence and Vaishali's age 4 years ago :

$\dfrac{14}{2}=\dfrac{7}{1}=7:1$

∴The ratio between Sara's age  4 years hence and Vaishali's age 4 years ago is 7:1  .

# Learn more :

The ages of A and B are in the ratio 9 ratio 4 ,7 years hence the ratio of their ages will Age 5 ratio 3 find the present age​

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