Question

at present a mother is twice as old as his daughter. twenty years back their ages were in the ratio of 10 : 3 .The present age of the mother is​

Answer 1

Answer:

the present age of the mother is 70

i hope this helps!!

Step-by-step explanation:

let us take the present age of the mother as x and the present age of her daughter as y

• "at present a mother is twice as old as her daughter" so,
• we get the first equation as $x = 2y$ from this.
• "twenty years back their ages" Now, 20 years ago, their ages will be 20 years less., so, the past age of the mother is 20-x and the past age of the daughter is 20-y
• "twenty years back their ages were in the ratio of 10 : 3" since ratio is a fraction, we can say that  $\frac{20-x}{20-y} = \frac{10}{3}$

substituting the $x$ with the first equation so we get:

$\frac{20-(2y)}{20-y} = \frac{10}{3}$

now we cross multiply, which gives us,

=> $3(20-2y) = 10(20-y)$

=> $60 - 6y = 200 - 10y$

=> $- 6y + 10y = 200 - 60$

=> $4y = 140$

=> $y = \frac{140}{4}$

=>$y = 30$

to find the mothers present age, we use the first equation;

$x = 2y$

$x = 2$×$35$

$x = 70$