Question

The incomes of "Tom Cruise" and "Richard Gere" are in the ratio 3:4. Their expenditure
are in the ratio 3: 5. If each saves Rs. 1,500. Find their incomes.​

Answer 1

Step-by-step explanation:

Given :-

The incomes of "Tom Cruise" and "Richard Gere" are in the ratio 3:4. Their expenditure are in the ratio 3: 5 and each saves Rs. 1,500.

To find :-

Find their incomes?

Solution :-

Given that :

The ratio of the incomes of Tom Cruise and Richard Gere = 3:4

Let they be 3X and 4X

Let the income of Tom Cruise be Rs. 3X

Let the income of Richard Gere be Rs. 4X

The ratio of their expenditure = 3:5

Let they be 3Y and 5Y

Let the expenditure of Tom Cruise be

Rs.3Y

Let the expenditure of Richard Gere be Rs. 5Y

The saving of each one = Rs. 1500

We know that

Income - Expenditure = Saving

Saving of Tom Cruise

=> 3X-3Y = 1500

=> 3(X-Y) = 1500

=> X-Y = 1500/3

=> X-Y = 500 -----------(1)

=> X = 500+Y ----------(2)

and

Saving of Richard Gere

=> 4X-5Y = 1500 -----(3)

On Substituting the value of X in (3) from (2)

=> 4(500+Y) -5Y = 1500

=> 2000+4Y-5Y = 1500

=> 2000-Y = 1500

=> -Y = 1500-2000

=> -Y = -500

=> Y = 500 -----------(4)

On Substituting the value of Y in (2) then

=>X = 500+500

=> X = 1000----------(5)

Now , 3X = 3(1000)=Rs.3000

4X = 4(1000)=Rs. 4000

and

3Y = 3(500)=Rs.1500

5Y=5(500)=Rs. 2500

Their incomes = Rs. 3000 and Rs. 4000

Their expenditures = Rs. 1500 and Rs. 2500

Answer:-

Income of Tom Cruise = Rs. 3000

Income of Richard Gere = Rs. 4000

Check :-

Their incomes = Rs. 3000 and Rs. 4000

Their expenditures = Rs. 1500 and Rs. 2500

Saving of Tom Cruise

= Rs.3000-Rs. 1500

= Rs. 1500

and

Saving of Richard Gere

= Rs. 4000-Rs.2500

=Rs. 1500

Their savings Rs. 1500 each

Verified the given relations in the given problem.

Used Method:-

• Substitution method

Used formulae:-

• Income - Expenditure = Saving