Aptitude Discussion

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 |

**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.**

**Viswanath Annangi**

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**Bhawar**

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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**

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

**Sravan Reddy**

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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**

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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..

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

**Lisa**

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

Can anyone will please elaborate this?

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

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

**Shikha**

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

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

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