Question

Five years ago, the sum of the ages of Vishal and
Vicky was 65 years. Vishal's age four years ago was
equal to two times Vicky's age eight years ago. Find
the age of Vicky, nine years hence (in years).​

Answer 1

Question:

Five years ago, the sum of the ages of Vishal and Vickey was 65 years. Vishal's age 4 years ago was equal to 2 times Vicky's age 8 years ago. Find the age of Vicky 9 year hence.

Answer:

Vicky's age 9 years ago was 20 years.

Solution:

Let the present age of Vishal be x years and the present age of Vicky be y years.

Thus,

Age of Vishal 5 years ago = (x-5) years

Age of Vicky 5 years ago = (y-5) years

Now,

According to the question,

Five years ago, the sum of the ages of Vishal and Vickey was 65 years.

Thus,

=> (x-5) + (y-5) = 65

=> x + y - 10 = 65

=> x + y = 65 + 10

=> x + y = 75

=> x = 75 - y ------------(1)

Also,

Age of Vishal 4 years ago = (x-4) years

Age of Vicky 8 years ago = (y-8) years

Now,

According to the question,

Vishal's age 4 years ago was equal to 2 times Vicky's age 8 years ago.

Thus,

=> (x - 4) = 2(y - 8)

=> x - 4 = 2y - 16

=> x = 2y - 16 + 4

=> x = 2y - 12 -----------(2)

Clearly,

From eq-(1) and eq-(2) , we have;

=> 75 - y = 2y - 12

=> 2y + y = 75 + 12

=> 3y = 87

=> y = 87/3

=> y = 29

Now,

Putting y = 29 in eq-(1) , we get;

=> x = 75 - y

=> x = 75 - 29

=> x = 46

Hence,

The present age of Vishal = 46 years

The present age of Vicky = 29 years

Also,

Age of Vicky, 9 years ago

= (29-9) years

= 20 years

Answer 2

Answer

GiveN

Five years ago, the sum of the ages of Vishal and Vicky was 65 years. Vishal's age four years ago was equal to two times Vicky's age eight years ago.

To FinD

Find the age of Vicky.

HencE

1. Let M be the age of Vishal.
2. Let N be the age of Vicky.
3. Let M - 5 be the age of Vishal.
4. Let N - 5 bw the age of Vicky.

65 is the age of Vishal and Vicky five years ago.

HencE

$\bf = ( M - 5 ) + (N - 5 ) = 65 \\ </p><p>\bf = M + N - 10 = 65 \\ </p><p>\bf = M + N = 65 + 10 \\ </p><p>\bf = M + N = 75 \\ </p><p>\bf = M = 75 - N \: \: equation \: 1$

M - 4 = age of Vishal four years ago.

N - 8 = age of Vicky eight years ago.

HencE

Given question 2 times age of Vishal is Vickys age ( 2 × 4 = 8 )

HencE

$\bf = (M - 4) = 2 (N - 8) \\ </p><p>\bf = M - 4 = 2N - 16 \\ </p><p>\bf = M = 2N - 16 + 4 \\ </p><p>\bf = M = 2N - 12 \: \: equation \: 2</p><p>$

Equation 1 and Equation 2

$\bf = 75 - N = 2y - 12 \\ </p><p>\bf = 2N + N = 75 + 12 \\ </p><p>\bf = 3N = 87 \\ </p><p>\bf = N = \frac{87}{3} </p><p>\bf = N = 29 \: \: equation \: 3$

Adding ( y = 29 ) for equation - 1

$\bf = M = 75 - N \\ \bf = M = 75 - 29 \\ \bf = M = 46 \: \: equation \: 4$

So, 29 is age of Vicky and 46 is age of Vishal.

( 29 - 9 = 20) Therefore, 20 is the answer and 20 is the age of vicky 9 years ago.