Question

The ages of Hari and harry are in the ratio 5:7.four years from now the ratio of there ages will be 3:4. find there present ages hari

Answer 1

AnswEr :

Let the Present Age of Hari and Harry be 5n and 7n respectively.

$\bold{4 \: Yrs. \: from \: Now} \begin{cases}\sf{Hari=5n + 4} \\ \sf{Harry=7n + 4}\end{cases}$

• According to the Question Now :

$\leadsto \sf\dfrac{Hari \: Age}{Harry \: Age} = \dfrac{3}{4}$

$\leadsto \sf\dfrac{5n + 4}{7n + 4} = \dfrac{3}{4}$

$\leadsto \sf 4 \times (5n + 4) = 3 \times (7n + 4)$

$\leadsto \sf 20n + 16 = 21n + 12$

$\leadsto \sf 16 - 12 = 21n - 20n$

$\leadsto \boxed{\sf n = 4}$

_________________________________

• Present Age of Hari and Harry is :

◗ Hari = 5n = 5 × 4 = 20 Years

◗ Harry = 7n = 7 × 4 = 28 Years

⠀

∴ Therefore, Present Age of Hari and Harry is 20 Years and 28 Years respectively.

Answer 2

$\LARGE\underline{\underline{\sf \red{G}\blue{i}\green{v}\orange{e}\red{n}:}}$

• Age of Hari : Harry are in ratio = 5:7 (present)
• After four years ratio will be = 3:4

$\textsf{</strong><strong>Lets</strong><strong> </strong><strong>Try</strong><strong> </strong><strong>to</strong><strong> </strong><strong>Solve</strong><strong> </strong><strong>by</strong><strong> </strong><strong>Basic</strong><strong> </strong><strong>Method</strong><strong> </strong><strong>First</strong><strong>}$

Let Their Present age be = 5x & 7x .

After 4 years, Hari will be = (5x+4) years old .

After 4 years, Harry will be = (7x+4) years old .

And it is Given that their Ratio will be 3:4 .

So, According to Question Now,

$\frac{5x + 4}{7x + 4} = \frac{3}{4} \\ \\ cross - multiply \\ \\ 20x + 16 = 21x + 12 \\ \\ 21x - 20x = 16 - 12 \\ \\ x = 4$

So,

5x = 5 × 4 = 20

$\large\red{\boxed{\sf Present\:age\:of\:</strong><strong>Hari</strong><strong>=</strong><strong>2</strong><strong>0</strong><strong>years}}$

7x = 7 × 4 = 28

$\large\</strong><strong>g</strong><strong>r</strong><strong>e</strong><strong>e</strong><strong>n</strong><strong>{\boxed{\sf Present\:age\:of\:</strong><strong>Harry</strong><strong>=</strong><strong>2</strong><strong>8</strong><strong>years}}$

$\rule{200}{4}$

$\</strong><strong>L</strong><strong>a</strong><strong>r</strong><strong>g</strong><strong>e</strong><strong>\boxed{\fcolorbox{fuchsia}{grey}{Solution</strong><strong>(</strong><strong>2</strong><strong>)</strong><strong>}}$

$\textsf{</strong><strong>Lets</strong><strong> </strong><strong>Try</strong><strong> </strong><strong>it</strong><strong> </strong><strong>with</strong><strong> </strong><strong>Ratio</strong><strong> </strong><strong>Method</strong><strong> </strong><strong>Now</strong><strong>}$

we know that, present ratio = 5:7

After 4 years it will be = 3:4

or,

we can write ,,

Present Ratio = 5 : 7

After 4 years = 2(3 : 4) = 6 : 8

(6-5) = (8-7) = 4 years

1 unit Ratio = 4 years

so,

5 unit ratio = 5 × 4 = 20 years = Hari Present Age ......

7 unit ratio = 7 × 4 = 28 years = Harry Present Age .....

$\huge\underline\mathfrak\green{Hope\:it\:Helps\:You}$