Question

sunita is twice as old as Ashima. if six years is subtracted from Ashima's age and four years is added to sunita's age then sunta will be four times Ashima's age.How old were they two​

Answer 1

Given :-

 

• Sunita is twice old as Ashima  

Condition :-  

• If six years is subtracted from Ashima's age and four years is added to Sunita's age then Sunita will be four times Ashima's age.

To find :-  

• How old were they two  ?

Solution :-  

 

~Here , first we need to assume their ages in variable and then write them according to the given conditions to find their ages .

__________

 

• Let Ashima’s age be ‘ x ‘  

• Then Sunita’s age will be ‘ 2x ‘  

__________

According to the given condition ::  

• Six years subtracted from Ashima’s age  

   x – 6  

• Four years are added to Sunita’s age  

   2x + 4  

• Then ,  

$\sf \implies ( 2x + 4 ) = 4( x - 6 )$

$\sf \implies 2x + 4 = 4x - 24$

$\sf \implies 4x - 2x = 24 + 4$

$\sf \implies 2x = 28$

 

$\sf \implies x = \dfrac{28}{2}$

$\sf \implies x = 14$

Therefore  

• Age of Sunita  

= 2x  

= 2( 14 )  

= 28 years  

• Age of Ashima  

= x

= 14 years  

Sunita’s age is 28 years and Ashima’s age is 14 years  

Answer 2

⠀⠀⠀⠀⠀⠀${\rm{\purple{\underline{\underline{★Required \:Answer★}}}}}$

Ashima's age = 14 years

Sunita's age = 28 years

⠀⠀⠀⠀⠀${\rm{\pink{\underline{\underline{★Solution★}}}}}$

${\rm{\red{\underline{\underline{Given : }}}}}$

• Sunita is twice as old as Ashima
• If six years is subtracted from Ashima's age and four years are added to Sunita's age subsequently then the age of Sunita will be four times the age of Ashima.

${\rm{\blue{\underline{\underline{To \: Find: }}}}}$

• Present ages of Ashima and Sunita.

${\rm{\green{\underline{\underline{Description : }}}}}$

Here, let the present age of Ashima be x years and present age of Sunita be y years. Form the equation using given conditions in question. We will get two equations containing two variables as x and y. Solve the two equations using the substitution method, and find the values of x and y. Find their ages two years ago and add them to get the result.

${\rm{\orange{\underline{\underline{Calculations : }}}}}$

Let Ashima's present age = x years

According to the first given condition that is, Sunita is twice as old as Ashima.

Therefore,

y = 2x ⠀⠀⠀⠀⠀..eq.(1)

Given, if six years is subtracted from Ashima's age and four years added to Sunita's age, then Sunita will be four times that of Ashima's age.

Therefore,

$\longrightarrow \rm4 \times (x - 6) = y + 4$

$\longrightarrow \rm4x - 24 = y + 4$

$\longrightarrow \rm 4x - y = 4 + 24$

$\longrightarrow \rm 4x - y = 28 \: \: \: \: \: \: \: \: ..eq.(2)$

Now, putting value of y from equation (1) in equation (2), we get :-

$\longrightarrow \rm 4x - 2x = 28$

$\longrightarrow \rm 2x = 28$

$\longrightarrow \rm x = \frac{28}{2}$

$\longrightarrow \rm x = \frac{ \cancel{28}}{\cancel{2}}$

$\longrightarrow \rm x = 14 \: years$

Thus, Ashima's present age is 14 years.

Putting value of x in equation (i), we have :-

$\longrightarrow\rm y = 2 \times 14$

$\longrightarrow \rm y = 28 \: years$

∴ Sunita's present age is 28 years.

Hence, Present ages of Ashima and Sunita are 14 and 28 years respectively.