Aptitude - Problems on Ages - Discussion

@All.

Here's my solution:.

Here, We need Anand's age.
So first we check the multiple of 4 we get (24, 40) by using elimination.
After 3 years, the new ratio is 11:9 the options become (24+3, 40+3) = (27, 43) the 9 multiple is 27.
So the answer is 27.

Present ages:

Sameer = x.
Anand = y.

x/y = 5/4 -------->eq(1)

After 3 yrs:
x + 3/y + 3 = 11/9 -----------> eq(2)

Solving equations 1 and 2 we get,

9x - 11y = 6,
4x - 5y = 0,
x = 30 and y = 24.

5:4
11:9.

The difference between 5 and 11 is 6.
The difference between 4 and 9 is 5.The differences are not same.
So We have to multiply the difference between 5:4(5-4=1) with 11:9 as 1*(11:9) and the difference between 11:9(11-9=2) with 5:4 as 2(5:4).
Finally, we get as;
10:8
11:9 here the difference is 1.
1p= 3years then,
8p = 24 years is the final answer.
So, Anand's age is 24 years.

Let the present age of Sameer and Anand be x and y.

x:y=5:4.

therefore,
x/y = 5/4.
x=5y/4 ----> (1).

After 3 years ratio becomes:

x+3 : y+3 = 11:9.
x+3/y+3 = 11/9.

By cross multiplying.

9 (x+3) = 11 (y+3).
9x+27=11y+33.
9x-11y = 5.

put x=5y/4 in above eq.
9 (5y/4) -11y =5.
45y-44y/4 = 5.
y = 5*4= 20.

put y in eq 1.
x = 5y/4 = 5 (20) /4 =25.

balancing the condition 25/20 = 5/4 or 5 :4.

Let the present age of Sameer and Anand be x and y.

x : y = 5 : 4.

Therefore,
x/y = 5/4.
x = 5y/4 ----> (1).

After 3 years ratio becomes:

x+3 : y+3 = 11:9.
x+3/y+3 = 11/9.

By cross multiplying.

9 (x+3) = 11 (y+3).
9x + 27=11y+33.
9x - 11y = 5.

Put x = 5y/4 in above eq.
9 (5y/4) -11y =5.
45y-44y/4 = 5.
y = 5*4= 20.

put y in eq 1.
x = 5y/4 = 5 (20) /4 =25.

Balancing the condition 25/20 = 5/4 or 5 :4.

Very helpful. Thanks, everyone for explaining the answer.

best tricks for this type of question;

5 :4.
11:9.

4(years Anand age question ask Anand age then multiply)*3(years hence)*2(11-9=2)/(5*9 cross multiply) - (11*4 cross multiply) = 24.

So, the answer = 24.

Always we have to assume (in ratio problem): X.

And according to the question the present age is = 5X/4X.

And;
According to the question 3 year hence so we can write in form as 5X + 3/4X + 3.

And our next step will be according to the question said the ratio will become 11/9.
So we can write'
5x+ 3/4x+3 = 11/9.

After solving equations
45x + 27 = 44x + 33 and then;
X = 6. After solving that equations
And put the value in Anand age so;
The question will be;
4x = 4*6 = 24 that is final answer.

We can also use the formula qt(r-s)/ps-qr where p,q,r,s are given ratios 5:4, 11:9 respectively and t= years given.

4(3)(11-9)/5(9)-4(11) = 12(2)/45 - 44 = 24.

Formula: The ratio of present ages of A and B is p:q and after t years, the ratio is r:s, then
A's present age = pt(r-s)/ps-qr.
B's present age = qt(r-s)/ps-qr.

At last, they have multiplied with 4 that is 4x because they have considered the present age of Anand is 4x we have been asked to find present age of Anand that's why we have multiplied with 4 and we know x=6.

So, 4 * 6 = 24.