Aptitude - Problems on Ages - Discussion

Calculation can be reduced by using components and dividend which is applied on ratio's on both sides of equals.

Here is the method -> num1/den1 = num2=den2.
-> APPLYING COMPONENDO AND DIVIDENDO ON BOTH SIDES.
-> (num1+den1)/(num1-den1) = (num2+den2)/(num2-den2).

So here it goes,
(5x + 3) / (4x +3) = 11/9,
using above method it reduces to below in one go,
(9x + 6) / x = 10,
=> x = 6.

The requires answer then would be 4*x (using given ratio) is 24(answer).

@Murugan k.

QUE--> 5 years ago A age was 3 times as old as B . If A is 30years older than B .The present age of A?

Answer--> Before 5 years A=3B.

So after 5 years A's age increases by 5 so does the B's age. We get
A+5 = 3B+5-----------(eqn1)(this is present because I have increased 5yr from past).

A is 30 year older than B so A=B+30--------(eqn2),

Since we have to find the value of A we convert(eqn2)cas B=A-30--------(eqn3).

Now substitute (eqn3)in(eqn1).

A+5 = 3(A-30)+5.

A = 3A-90.

2A = 90.

A = 45 and B = 15.

I think here is an error in answer,

If anand present age is 24(as 4 * 6 = 24, sameer age would be 5 * 6 = 30), here as mentioned in the question the ratio of their present age should be 11/9, but here the ratio according to the ans would be 30/24=5/4(5:4)(as per present age).

But we need to get 11/9 as the ration.

Anands present age would be 4x + 3 = 4*6+3=24+3 = 27.
And Sameer present age would be 5x + 3 = 5*6+3 = 33.
Then the ratio will satisfy, as 33/27 = 11/9(11:9 present ratio).

Can anyone justify existing answer.

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.

Let the present ages of Sameer and Anand be X and Y.

Also given in question x and y are in the ratio 5 : 4 then, X/Y = 5/4 ---> eq [1]
After 3 years hence(later) & their ratios are = x + 3/y + 3 = 11 : 9.
9(x + 3) = 11(y + 3),
9x + 27 = 11y + 33,

9x - 11y = 6---> eq[2].
Ffrom eq [1], x = 5y/4 --> eq [3].
Substitute eq [3] in eq [2].

9(5y/4) - 11y = 6,
45y - 44y = 24,
1y = 24,
Then, y = 24. the present age of Anand(y) is 24.

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 me explain this in a simple procedure. The First ratio is 5:4.
We have to find Anand age after 3yrs.
Second ratio 11:9
So add 3 to both the numbers.y we r adding 3 is in question they gave after 3yrs
So the new ratio is 14:12

First ratio is 5:4.
New ratio is 14:12.
In this Anand age ratio is 4 AND 12.

Now check the option which is exactly divisible by both the numbers and that's the answer.

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 me make it simple for you guys.

First, solve make ratios then equation:
5:4, which is 5x for Sameer and 4x for Anand : 5x/4x.

Three years from now 5x+3/4x+3 =11/9, solving this equation you get x=4.
How put 4 back on x places which is 5(4)/4(4)= 30/24 you get,

Hence 30/24 divide by 6 you get 5/4 further if u add 3 years from now, which 33/27, divide it by 3 you get ratio of 11/9.

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.