Question

The ages of Ajay and Bhaskar are in the ratio 5:7.Five years from now, the ratio of their ages will be 5:6. Find their present ages.​

Answer 1

Given :

• The ages of Ajay and Bhaskar are in the ratio 5:7 .
• Five years from now, the ratio of their ages will be 5:6 .

To Find :

• Present Age of Ajay and Bhaskar .

Solution :

$\longmapsto\tt{Let\:Present\:age\:of\:Ajay\:be=5x}$

$\longmapsto\tt{Let\:Present\:age\:of\:Bhaskar\:be=7x}$

After 5 years :

$\longmapsto\tt{Age\:of\:Ajay=5x+5}$

$\longmapsto\tt{Age\:of\:Bhaskar=7x+5}$

A.T.Q :

$\longmapsto\tt{\dfrac{5x+5}{7x+5}=\dfrac{5}{6}}$

$\longmapsto\tt{6(5x+5)=5(7x+5)}$

$\longmapsto\tt{30x+30=35x+25}$

$\longmapsto\tt{30x-35x=25-30}$

$\longmapsto\tt{-5x=-5}$

$\longmapsto\tt{x=\cancel\dfrac{-5}{-5}}$

$\purple\longmapsto\:\large\underline{\boxed{\bf\blue{x}\pink{=}\red{1}}}$

Value of x is 1 .

Therefore :

$\longmapsto\tt{Present\:Age\:of\:Ajay=5(1)}$

$\longmapsto\tt\bf{5\:yrs}$

$\longmapsto\tt{Present\:Age\:of\:Bhaskar=7(1)}$

$\longmapsto\tt\bf{7\:yrs}$

Answer 2

Solution :-

BASIC METHOD :-

Let us assume that, the present age of Ajay is 5x years and present age of Bhaskar is 7x years .

So,

→ Age of Ajay 5 years from now = (5x + 5) years .

and,

→ Age of Bhaskar 5 years from now = (7x + 5) years .

A/q,

→ (5x + 5) : (7x + 5) = 5 : 6

→ (5x + 5)/(7x + 5) = 5/6

→ 6(5x + 5) = 5(7x + 5)

→ 30x + 30 = 35x + 25

→ 35x - 30x = 30 - 25

→ 5x = 5

→ x = 1 years .

therefore,

→ Present age of Ajay = 5x = 5 * 1 = 5 years .

→ Present age of Bhaskar = 7x = 7 * 1 = 7 years .

Hence, Present Age of Ajay is 5 Years and Present Age of Bhaskar is 7 Years .

RATIO METHOD :-

⋆ Present Age⠀⠀➞ 5 Yrs.⠀⋆ Future Age

Ajay : Bhaskar⠀⠀⠀⠀⠀⠀⠀⠀⠀Ajay : Bhaskar

⠀⠀5 : 7⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 5 : 6

◗ Difference of both Ratios is :-

→ (7 - 5) = 2 and, (6 - 5) = 1 .

we will Multiply them by Opposite terms. Means by 1 in Present age ratio and By 2 in Future age ratio to make Difference Equal.

⠀⠀5 : 7⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀5 : 6

× 1 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀× 2

_______________________________

⠀⠀5 : 7⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀10 : 12

Now, Difference Between Ratios are Same, i.e. (10 - 5) = (12 - 7) = 5

So, we will find the Difference of Ratio in Ages, that Means we can find from like Ajay (10 - 5) = 5 or, Bhaskar (12 - 7) = 5.

Divide Year Gap By that Number.

↦ Year Gap / Difference of Age

↦ 5 Years / 5

↦ 1

Now, Just Multiply the Outcome (1 in this Case) with ratio to Find Present Age :

◗ Ajay = (5 × 1) = 5 Years .

◗ Bhaskar = (7 × 1) = 7 Years .

∴ Present Age of Ajay is 5 Years and Present Age of Bhaskar is 7 Years .

Learn more :-

what is the sum (in Rs) which when divided among A, B, C, D in the proportion 2:3:5:8 provides Rs 8420 less to D the wha...

https://brainly.in/question/26704366

two vessels x and y of capacities one and two litres respectively and completely filled with mixtureof two chemicals a a...

https://brainly.in/question/26618169