The monthly income of two persons are in the ratio 6 : 8 & their expen

Question

The monthly income of two persons are in the ratio 6 : 8 & their expenditure are in the ratio 14 : 19. If each saves $80 per month, what is the sum of their monthly incomes ?

(A) 900
(B) 1400 
(C) 2600 
(D) 2800
(E) 3000

priyachandank · Answer

Has someone got the answer as mentioned? If so Please share the steps? thank you.

Alligator16 · Answer

Equation: Income - Expense = Savings

For Person 1: 6x - 14y = 80 -------equation i
For Person 2: 8x - 19y = 80 -------equation ii

After solving both equation, we will get: x = 200 and y = 80

Sum of their monthly income = 6x + 8x = 14x

14x200 = 2800

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Abhibarua · Answer

Let their incomes be 6x and 8x, and their expenditures be 14y and 19y respectively.

Given, 6x - 14y = 80    
And, 8x - 19y = 80

Multiply Eq. 1 by 19 and Eq. 2 by 14 to get,

(6*19)x - (14*19)y = (80*19)    
And, (8*14)x - (19*14)y = (80*14)

Subtract Eq. 4 from Eq. 3 to get,

114x - 112x = 80 (19-14)
2x = 400
x = 200

So, 6x+8x = 14x = 14*200 = 2,800 (Option: D)

rohanc8790 · Answer

I used a different way for solving this..

We know that since the ratio of their income is 6:8, the total portion of their income will be 6+8=14.

Now, because the question asks for the total salary of the two people, that would mean that the answer needs to be a multiple of 14 (as their cannot be any reminder)

That narrows down our scope of work.

There are only two numbers in the answer options that are divisible by 14, ie. Option B- 1400 and Option D- 2800.

Let's try to work with the first one.

Let the income of the two folks be 6x and 8x

Therefore,  6x+8x=1400 =>x=100

So the two incomes are 600 and 800

That would mean that the two expenditure amounts will be  600-80= 520  and  800-80=720.

When we check the expenditure ratio, it should be \frac{14}{19} in its simplest form.

\frac{520}{720}  does not give us that answer.

Hence the only option is option D, or 2800

You can do the same process with 2800. It will end up matching. But you don't need to

shohan2722 · Answer

I would rather solve this by manipulating the ratios in a way such that the difference between the ratio of income and expenditure of both persons become equal. Why? Because they have equal savings. To do so, I'll multiply 6:8 with 5 (the difference of 14 and 19) and I'll multiply 14:19 with 2 (the difference of 6 and 8). Thus the income ratio becomes 30:40 and the expenditure ratio becomes 28:38. And the saving ratio becomes 2:2 which perfectly aligns with the conditions of the question. So by using basic ratio method, we have, 2 equals 80$ (given) thus 30 equals 1200 and 40 equals 1600 and their sum equals 2800$

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The monthly income of two persons are in the ratio 6 : 8 & their expen

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