Question

Rohit's monthly expenditure is 20% more than Shivani's monthly income. Shivani's monthly expenditure is
20% less than the monthly income of Dhankar. Rohit's monthly expenditure is 50% more than that of
Dhankar's monthly income. If the monthly savings of Shivani is Rs. 7200. fmd the monthly income (in
rupees) of Shivani?
20000
15000
30000
25000​

Answer 1

Answer:

20000

Step-by-step explanation:

try with the options. then you can solve this .

another way may be possible but I don't know.

so, please excuse me

Answer 2

Shivani's monthly income will be Rs.20000

Step-by-step explanation:

Given:

Rohit's monthly expenditure=20% more than Shivani's monthly income

Shivani's monthly expenditure=20%less than Dhankar's monthly income

Rohit's monthly expenditure=50% more than Dhankar's monthly income

Shivani's monthly savings=Rs.7200

To find:

Shivani's monthly income in (Rs.)

Solution:

Let's assume Shivani's monthly income as 100x & Dhankar's monthly income as 100y

According to condition 1

⇒Rohit's monthly expenditure=20% more than Shivani's monthly income

assuming Shivani's monthly income is 100x

∴ Rohit's monthly expenditure= 20% of 100x + 100x

                                                  =$\frac{20}{100}.100x^{} +100x$

Rohit's monthly expenditure= 20x+ 100x

∴ Rohit's monthly expenditure=120x.....................(1)

According to condition 2

Shivani's monthly expenditure=20% less than Dhankar's monthly income

assuming Dhankar's monthly income is 100y

∴ Shivani's monthly expenditure =  100y-20% of 100y

                                                      =$100y-\frac{20}{100}.100y$

Shivani's monthly expenditure = 100y -20y

∴ Shivani's monthly expenditure = 80y......................(2)

As we know,

Savings= Income- Expenditure

∴ Shivani's monthly savings = Shivani's monthly income-(Shivani's      monthly expenditure)

∴ 7200 = 100x- 80y....................[from given and (2)]

Dividing the equation by 20, we get

360= 5x+4y........................(3)

According to condition 3

Rohit's monthly expenditure=50% more than Dhankar's monthly income

assuming Dhankar's income is 100y

∴ Rohit's monthly expenditure= 50% of 100y + 100y

Rohit's monthly expenditure= $\frac{50}{100}.100y+100y$

Rohit's monthly expenditure = 50y+100y

∴ Rohit's monthly expenditure= 150y...................(4)

Hence, from (1) and (4) we get

120x=150y

∴ 120x-150y=0

Dividing the equation by 30, we get

4x-5y=0.....................(5)

Now multiplying equation (3) by 5 & equation (5) by 4, we get

25x-20y=1800..........(6)

16x-20y=0..................(7)

Subtracting equation (7) from equation (6)

25x- 20y = 1800

16x- 20y  =   0  

(-)    (+)         (-)    

9x          = 1800................................(25x-16x=9x, -20y+20y=0, 1800-0=1800)

∴ x= 1800/9

∴ x=200

Thus, Shivani's monthly income=100x

                                                    =100(200)

∴ Shivani's monthly income= Rs 20000