Question

The present ages of A and B are in the ratio 7 : 4. Six years hence, the ratio of their ages will be 10 : 7. The present ages of A and B are:​

Answer 1

Answer:

let the ages of a and b be 7x and 4x six year later +6

ratio 10x and 7x

7x+4x+12=10x+7x

12x+12=17x

12=17x-12x

Answer 2

Answer -

• The present age of A = 14 years.
• The present age of B = 8 years.

To find -

• The present ages of A and B.

Step-by-step explanation -

• It is given that the present ages of A and B are in the ratio 7 : 4.

So let -

• The present ages of A and B be "7x" and "4x" years respectively.

Six years hence -

• A's age will be "7x + 6" years.
• B's age will be "4x + 6" years.

Given that -

• Six years hence, the ratio of the ages of A and B will be 10 : 7.

Therefore -

$\bf \longmapsto \: 7x + 6 : 4x + 6 = 10 : 7$

$\longmapsto \bf \: \dfrac{7x + 6}{4x + 6} = \dfrac{10}{7}$

$\longmapsto \: \bf10 \: (4x + 6) = 7 \: (7x + 6)$

$\longmapsto \: \bf40x + 60 = 49x + 42$

$\longmapsto \: \bf40x - 49x = 42 - 60$

$\longmapsto \bf \: - 9x = - 18$

$\longmapsto \: \bf x = \dfrac{ - 18}{ - 9}$

$\longmapsto \: \bf x = 2$

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Hence -

$\sf A's \: present \: age = 7x = 7 \times 2 = 14 \: years.$

$\sf B's \: present \: age = 4x = 4 \times 2 = 8 \: years.$