Question

At the present age of a father and his son are in the ratio 7:3 ,and they will be in the ratio 2:1 after 10 years. Then the present age of father is
a) 42
b) 56
c) 70
d) 77

Answer 1

Answer: c)70

Step-by-step explanation:

Let present age of father and son be = 7x and 3x.

After 10 years Father will be = (7x+10)

After 10 years Son will be = (3x+10)

so,

according to Question their ratio will be 2:1

solving this ,

Hence Present age of Father = 7x = 7×10 = 70 years (Option C) .

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Lets try it with ratio Method now :------

Present ratio F : S = 7:3

10years later ratio F:S = 2:1

multiplying Present ratio by 1 and multiplying 10 years ratio by 4 we get,

(7:3)×1 = 7 : 3

(2:1)×4 = 8 :4

Now, difference of ratio is same ,

(8-7) = (4-3) = 1

Hence , this 1 unit ratio is given 10 years later .

so,

1 unit ratio ----------------- 10 years .

7 unit ratio(Present age of Father) ---------- 70 years .

so, present age of Father is 70 years..

Answer 2

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

Given :-

• The present ages of the father and the son are in the ratio of 7:3
• After 10 years, the ratio will become 2:1

To find :-

• Their present ages

Solution :-

Let the present age of the father be = 7x.

And let the present age of the son be = 3x.

Now, we are given the relationship of the the ages of the father and the son after 10 years.

So, from the given information we can say after 10 years their ages will be,

Father = 7x + 10

Son = 3x + 10

So,

$\leadsto\tt{\dfrac{7x+10}{3x+10}=\dfrac{2}{1}}$

Cross multiplying,

$\leadsto\tt{7x+10 = 2(3x+10)}$

$\leadsto\tt{7x+10 = 6x+20}$

$\leadsto\tt{7x - 6x = 20 - 10}$

$\leadsto\tt{\red{x = 10}}$

So,

The present age of the father is = 7 * 10 = 70 years.

The present age of the father is = 7 * 10 = 70 years.And the present age of the son is = 3 * 10 = 30 years.

$\rule{200}2$