Question

Income ratio of Ramesh and Suresh is 5:6. Their spending ratio is 7:9. Ramesh saves 4000 and Suresh saves 3000. Income and spending respectively of Ramesh and Suresh are

Answer 1

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

• Ratio of income of Ramesh and Suresh is 5:6.
• their Expenditures Ratio = 7:9
• Ramesh saves 4000 and Suresh saves 3000.

$\large\bf\underline {To \: find:-}$

• Income and expenditures of both Ramesh and Suresh.

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

Ratio of income of Ramesh and Suresh is 5:6

$\begin{cases} \tt \: </p><p> \text{Let income of Ramesh be 5x }\\ </p><p> \tt \text{Let income of Suresh be 6x }\end{cases}$

And Ratio of their expenditures is 7:9

$\begin{cases} \tt \: </p><p> \text{Let Ramesh expenditures be 7y }\\ </p><p> \text{Let Suresh expenditures be 9y }\end{cases}$

• ✝️ Savings = income - expenditures

Ramesh savings = 5x - 7y

»» 5x - 7y = 4000......(i)

Suresh savings = 6x - 9y

»» 6x - 9y = 3000.......(ii)

Multiplying eq .(i) by 6 and eq.(ii) by 5 we get,

»» 30x - 42y = 24000

»» 30x - 45y = 15000

⠀⠀-- ⠀⠀⠀+ ⠀⠀⠀--

━━━━━━━━━━━━━━━

⠀⠀⠀⠀⠀⠀3y = 9000

⠀⠀⠀⠀⠀⠀⠀y = 9000/3

• ⠀≫ y = 3000

➡️ Putting value of y = 3000 in eq.(i)

»» 5x - 7y = 4000

»» 5x - 7×3000 = 4000

»» 5x - 21000 = 4000

»» 5x = 4000 + 21000

»» 5x = 25000

»» x = 25000/5

• ≫ x = 5000

Now ,

»★ Ramesh income :-

• 5x = 5× 5000 = 25000

»★ Suresh income :-

• 6x = 6 × 5000 = 30000

≫ Ramesh expenditures :-

• 7y = 7×3000 = 21000

≫ Suresh expenditures :-

• 9y = 9×3000 = 27000

✝️hence , income and spendings of both Ramesh and Suresh is:-

• Ramesh:- 25000, 21000
• Suresh :-30000, 27000

Answer 2

$\sf{\underline{\red{\underline{Question:-}}}}$

Income ratio of Ramesh and Suresh is 5:6. Their spending ratio is 7:9. Ramesh saves 4000 and Suresh saves 3000. Income and spending respectively of Ramesh and Suresh are.

$\sf{\underline{\red{\underline{Given:-}}}}$

• Income ratio of Ramesh and Suresh is 5:6.
• spending ratio is 7:9.
• Ramesh saves 4000.
• Suresh saves 3000.

$\sf{\underline{\red{\underline{To\:Find:-}}}}$

• Income and spending respectively of Ramesh and Suresh are =?

$\sf{\underline{\red{\underline{Solution:-}}}}$

Let income ratio be = x

And expenditure be = y

so,

Income ratio of Ramesh and Suresh is 5x and 6x

ratio of expenditure of Ramesh and Suresh = 7y and 9y

$\sf{\underline{\red{\underline{According \:to\: Question:-}}}}$

We know

income - expenditure = savings

so,

Ramesh income = 5x-7y= 4000------equ(1)

suresh income = 6x-9y=3000-------equ(2)

Now , equalizing the equation .

in equ--(1) multiply by (6) and in equ---(2) multiply by (5)

$\sf{\underline{\red{\underline{We\:get:-}}}}$

$\sf→30x-42y=24000\\\sf→{\underline {_-30x_+42y=_-15000}}\\\sf→ 3y=9000\\\sf→y=\frac{9000}{3}\\\sf{\fbox{\underline{\purple{y=3000}}}}$

$\sf{\underline{\red{\underline{Now:-}}}}$

substitute the value of y equ(1)----

$\sf→5x-7y=4000\\\sf→ 5x-7×3000=4000\\\sf→ 5x-21000=4000\\\sf→5x=21000+4000\\\sf→5x=25000\\\sf→ x=\frac{25000}{5}\\\sf→ x=5000$

$\sf{\underline{\red{\underline{Therefore:-}}}}$

• Ramesh income=5x = 5×5000 = 25000
• suresh income = 6x= 6×5000 = 30000

And

• Suresh expenditure = 9y = 9×3000= 27000
• Ramesh expenditure = 7y = 7×3000= 21000