Question

Two years ago a mother was 4 times as old as
her son. Six years from now her age will
become more than double her son's age by 10
years. What is the present ratio of their ages ?
A) 2:1 B) 38:11
C) 19:7 D) 3:1​

Answer 1

Answer:

Let the present age of son be x

Then father's present age is 4x

Now,

According to question,

That is 10 years ago,

4x- 10 = 10 (x- 10)

4x -10=10x-100

100–10=10x-4x

90=6x

x=90/6

x=15

therefore,

Father=4x

=4*15

=60 years old

………………………………….…………………

Explanation in detail:

In the first line of the question we see that the question is talking about present ages therefore to start this one off we need simple algebra.Suppose that the sons age was x . Therefore fathers age would be 4 times sons age that's 4x.

In the second phase it talks about past or simply 10 years before the present time,Here we need to make an idea that when we are talking about past our ages will be less than the present time.So,to get the age for past we need to subtract 10 years form present age in this scenario.Fathers age would be 4x-10 and son's age would be x-10.

Third step,We now that to get the answer we need to equate things right? So as indicated in the question in past that's 10 years before the father was 10 times older then his son.

So its simple

4x-10= 10 *(x-10)

Step-by-step explanation:

Answer 2

Let present age of mother be "M" years and present age of son be "N" years.

Tow years ago a mother was 4 times aa old as her son.

• Age of mother = (M - 2) years
• Age of son = (N - 2) years

According to question,

=> M - 2 = 4(N - 2)

=> M - 2 = 4N - 8

=> M = 4N - 8 + 2

=> M = 4N - 6 _____ (eq 1)

Six years from now, her age become more than double her son's age by 10 years.

• Age of mother = (M + 6) years
• Age of son = (N + 6) years

According to question,

=> M + 6 = 2(N + 6) + 10

=> M + 6 = 2N + 12 +10

=> 4N - 6 + 6 = 2N + 22 [From (eq 1)]

=> 4N = 2N + 22

=> 2N = 22

=> N = 11

Put value of N in (eq 1)

=> M = 4(11) - 6

=> M = 44 - 6

=> M = 38

So,

Present age of mother = M

=> 38 years

Present age of son = N

=> 11 years

∴ Ratio of present age of mother and son is 38:11.

$\bold{\underline{Option\:B)\:38:11}}$