Question

16 years ago karthi's age was 7/8 times that of kamal. four years henece, karthi's age will be 5/6 that kamal. waht is the present age of karthi?​

Answer 1

Answer:

Two years ago, Aryan's age was seven times the age of karthik. Eight years hence, the age of aryan win be com twice the age of Karthik.

Answer 2

Given:

16 years ago Karthi's age was $\frac{7}{8}$ times that of Kamal.

Four years hence, Karthi's age will be $\frac{5}{6}$ that Kamal.

To find :

The present age of Karthi.

Solution:

Step 1 of 2:

Let, the present age of Karthi be 'x'.

The present age of Kamal be 'y'.

16 years ago Karthi's age was $\frac{7}{8}$ times that of Kamal.

x - 16 = $\frac{7}{8}$ (y - 16 )

8( x - 16 ) = 7 ( y - 16 )

8x - 128 = 7y - 112

8x - 128 - 7y + 112 = 0

8x - 7y - 16 = 0

8x = 7y + 16

x = $\frac{7y+16}{8}$

Four years hence, Karthi's age will be $\frac{5}{6}$ that Kamal.

x + 4= $\frac{5}{6}$ ( y + 4 )

6 ( x + 4 ) = 5 ( y + 4 )

6x + 24 = 5y + 20

6x - 5y  + 24 - 20 = 0

6x - 5y + 4 = 0

6x = 5y - 4

x = $\frac{5y - 4}{6}$

Step 2 of 2:

Equating both the x values,

$\frac{7y+16}{8}$ = $\frac{5y - 4}{6}$

6 ( 7y + 16 ) = 8 ( 5y - 4 )

42y + 96 = 40y - 32

42y - 40y = - 96 - 32

2y = 128

y = $\frac{128}{2}$

y = 64

x = $\frac{7y+16}{8}$

x = $\frac{7(64)+16}{8}$

x = $\frac{448+16}{8}$

x = $\frac{464}{8}$

x = 58

Final answer:

The present age of Karthi is 58 years