Algebra
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Q.

The ages of the two persons differ by 20 years. If 5 year ago, the older one be 5 times as old as the younger one, then their present ages, in year are:

 A.

25, 5

 B.

30, 10

 C.

35, 15

 D.

50, 30

 Hide Ans

Solution:
Option(B) is correct

Let the age be $x$ and $y$ years now.

Then, $x-y=20$ -------- (i)

and $(x-5)=5(y-5)$ ------- (ii)

On solving both equation we get:

$x = \textbf{30}$ and $y = \textbf{10}$

Edit: For an alternate approach, check comment by Nikhil

Edit 2: For another alternative approach, check comment by Sravan Reddy.

Edit 3: For yet another alternative approach, check comment by Bhawar.


(10) Comment(s)


Viswanath Annangi
 ()

the age difference between E and Y is E-Y=20 -------->1

5 Years ago the the younger ones age is Y=x ---------->2

5 years ago the elders ones age is E= 5x ------------->3

substitute equations 2 and 3 in Equation 1 you will get X=5 which is younger ones age 5 years ago.

so the present age of younger one (Y) is x+5 i.e 5+5 i.e 10

so the present age of elder one (E) is 5x+5 i.e 5*5+5 i.e 30



Bhawar
 ()

TRY TO UNDERSTAND IT THIS WAY

Let X and Y be present ages

Difference of them is x-y=20

Now Take both ages 5 years back

Which is x-5 and y-5

But the question also states that one was 5 times older then the other

Therefore

X-5 = 5(y-5)

Now solve the equation and you will get

30 and 10



Lokesh Boddeda
 ()

in 5years ago means its applicable to both old and younger



Sravan Reddy
 ()

My method (similar to what nikhil have mentioned above)

Subtract 5 from all solutions - (20,0),(25,5),(30,10),(35,15)

Now the answer should be one in which first age is 5 times second.

Same by checking options, its should be done at second option - 10 sec



Nikhil
 ()

Hi friends,

This can be solved easily by back up method ie..consider $A$ and $B$ are respective ages they differ by 20 so $A$ and $B+20$..

Now assume second option as you answer then..$A$ and $B+20$ become 10 and 10+20 from these we can conclude that 5 ago ages of yonger and older one are 5 and 25...

So now the answer is older ones age is 5 times of younger according to your qestion..

Check all option it's an easy method..


Prateek
 ()

Good one nikhil. But how is it faster than the one explained in the solution?


Lisa
 ()

I still do not understand why does $(x-5)=5(y-5)$ has been taken? Unsure

Can anyone will please elaborate this?


Sandy
 ()

If you don't know, try Nikhil's method. That is so simple.. :)

Sathya
 ()

because as it is mentioned in the question that ,5 yrs ago the older one is 5 times old than the younger one.


Shikha
 ()

why is it $(x-5)=5(y-5)$ ? why not $x=5(y-5)$?


Shresth
 ()

Because the ages of the two persons differ by 20 years. and as per the question, 5 year ago, the older one be 5 times as old as the younger one, not vice versa, that why Huh