Question

If the salary of sita and gita are in the ratio 4:5 and their expenses are in thd ratio of 6:7 .Find the ratio of their savings ,if gita manages to save a fourth of her salary

Answer 1

Answer:

20:35

Explanation:

Given:-Salary of sita and gita are in ratio 4:5 respectively

Their expenses are in ratio 6:7

Gita manages to save a fourth of her salary

To find;-Ratio of their savings

Solution:-

Let the income of sita and gits be 4x and 5x

And their expenditure be 6y and 7y

then their savings are 4x-6y and 5x-7y

5x-7y=5x/4

4(5x-7y)=5x

20x-28y=5x

20x-5x=28y

15x=28y

x=28y/15

Then ratio of their saving=4x-6y/5x-7y

Replacing x with 28y/15

4×(28y/15)-6y/5×(28y/15)-7y

112y/15-6y/140y/15-7y

22y/35y

22/35

22:35

__________

Therefore the ratio of their savings= 22:35

Answer 2

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

The ratio of their savings is 20:35

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

Given that :

Salary of sita and gita are in ratio 4 : 5.

Their expenses are in ratio 6 : 7.

Gita manages to save a fourth of her salary.

To Find :

The ratio of their savings.

Solution :

Let the income of sita and gits be 2x and 9x

Their expenditure be 3y and 5y

Their savings are 2x-3y and 9x-5y

So,

$\sf =>9x-5y=\dfrac{9x}{4}\\\\\sf =>4(7x-5y)=9x\\\sf =>20x-28y=9x\\\sf =>20x-9x=28y\\\sf =>15x = 28y\\\\\sf =>x=\dfrac{28y}{15}$

Then ratio of their saving = $\dfrac{2x-3y}{9x-6y}$

Replacing x with $\dfrac{28y}{15}$

=> 9x - 5y = 9x/4

=> 4(9x-5y) = 9x

=> 20x-28y = 9x

=> 20x - 9x = 28y

=> 15x = 28y

=> x = 28y/15

Now,

Ratio of their saving = 2x - 3y/9x-5y

Similarly here,

Replacing x with 28y/15

=> 4 × (28y/15) - 3y/5 × (28y/15) - 5y

=> 112y/15 - 3y/140y/15-5y

=> 22y/35y

=> 22/35

=> 22:35

Hence,

The ratio of their savings is 22 : 35.