Question

The monthly income of a and b in the ratio 8 ratio 7 and their expenditures are in the ratio 9 ratio 16 if each saves 5000 per month find the monthly income of it

Answer 1

$\large{\underline{\bf{\purple{correct\:Question:-}}}}$

The monthly income of a and b in the ratio 8:7 and their expenditures are in the ratio 19: 16 if each saves 5000 per month find the monthly income of each.

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$\large{\underline{\bf{\pink{Answer:-}}}}$

✰ A's monthly income = ₹24000.

✰B's monthly income = ₹ 21000

$\large{\underline{\bf{\green{Given:-}}}}$

✰ ratio of monthly income of A and B

= 8:7

✰ ratio of expenditure of A and B = 19:16

✰ Each one saves ₹ 5000 per month.

$\large{\underline{\bf{\green{To\:Find:-}}}}$

✰ we need to find the monthly income of A and B.

$\huge{\underline{\bf{\red{Solution:-}}}}$

Let the monthly income of A and B be ₹ 8x and ₹ 7x.

Let the expenditures be ₹ 19y and ₹ 16y.

Then,

monthly savings of A = ₹ (8x - 19y).

monthly savings of B = ₹ (7x - 16 y).

But monthly savings of both A and B is ₹ 5000.

$\bf\therefore\sf\:8x-19y=5000.......(i)$

$: \implies \sf\:7x-16y=5000.........(ii)$

Multiplying equation (ii) by 19,

and (i) by 16

$: \implies \sf\:(8x-19y=5000)\times16$

$: \implies \sf\:(7x-16y=5000)\times19$

we get,

133x -304y = 95000...........(iii)

128x -304y = 80000...........(iv)

Now solving (iii) and (iv) by Elimination method

133x -304y = 95000

128x -304y = 80000

--⠀⠀ ⠀+⠀⠀⠀⠀⠀--

5x⠀⠀⠀⠀⠀= 15000

x ⠀⠀⠀⠀⠀ =15000/5

$: \implies \sf\:{\purple{x= 3000}}$

So,

monthly income of A is ₹ 8x

$: \implies \sf\:8(3000)$

$: \implies \bf{\pink{\:24000}}$

monthly income of B is ₹ 7x

$: \implies \sf\:7(3000)$

$: \implies \bf{\pink{\:21000}}$

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Answer 2

Step-by-step explanation:

Correct Question :-

The monthly income of a and b in the ratio 8:7 and their expenditures are in the ratio 19:16 if each saves 5000 per month find the monthly income of it.

Solution :-

Given -

• The monthly income of A and B in the ratio 8:7
• Their expenditure are in the ratio 19:16
• Each saves ₹ 5000 per month

To Find -

• The monthly income

Let monthly income of A is ₹ 8x and B is ₹ 7x

Then,

Their expenditure is 19y and 16y

Now,

A saves 5000 per month

It means,

8x - 19y = 5000 ..... (i)

And

B saves 5000 per month

It means,

7x - 16y = 5000 ..... (ii)

Now, From (i) and (ii), we get :

→ [ 8x - 19y = 5000 ] × 7

[ 7x - 16y = 5000 ] × 8

→ 56x - 133y = 35000

56x - 128y = 40000

(-) (+) (-)

___________________

→ -5y = -5000

→ y = 1000

Now, Substituting the value of y on 8x - 19y = 5000, we get :

→ 8x - 19(1000) = 5000

→ 8x - 19000 = 5000

→ 8x = 5000 + 19000

→ 8x = 24000

→ x = 24000/8

→ x = 3000

Hence,

The monthly income of

A is 8x

→ 8 × 3000

→ ₹24000

And

B is 7x

→ 7 × 3000

→ ₹21000