Question

the ratio of ages of two boys is 5:6 after two years the ratio will be 7:8 the ratio of their ages after 12 years will be​

Answer 1

Answer:

17 /18

Step-by-step explanation:

ratio of ages of Boys A & B

A : B

Present age 5x : 6x

∴ after two years

∴5x+26x+2=78

40x + 16 = 42x + 14

2x = 2

x = 1

∴ Present age

A=5×1=5

B=6×1=6

After 12 years

A = 5 + 12 = 17

B = 6 + 12 = 18

AB= 17 / 18

Hope it will Help

Answer 2

S O L U T I O N :

Let the present age of one boy's be 5r & the present age of another be 6r respectively.

$\underbrace{\bf{2\:years\:later\::}}$

The age of one boy's will be = (5r + 2) years .

The age of another boy's will be = (6r + 2) years .

A/q

$\mapsto\tt{5r +2 :6r +2 =7:8}$

$\mapsto\tt{\dfrac{5r+2}{6r+2} =\dfrac{7}{8} }$

$\mapsto\tt{8(5r+2) = 7(6r+2) \:\:\:\underbrace{\sf{cross-multiplication}}}$

$\mapsto\tt{40r + 16 = 42r + 14 }$

$\mapsto\tt{40r- 42r = 14 -16}$

$\mapsto\tt{-2r = -2}$

$\mapsto\tt{r=\cancel{2/2}}$

$\mapsto\bf{r=1\:years}$

Thus;

The preset age of one boy = 5r = (5 × 1)= 5 years .

The preset age of another boy = 6r = (6 × 1)= 6 years .

Now;

$\underbrace{\bf{12\:years\:later\::}}$

The age of one boy's will be = (5+12) = 17 years .

The age of another boy's will be = (6 + 12) = 18 years .

One boy : another boy = 17:18 .