Question

ahe monthly income of Amit & Atul are in the ratio 6:5 .The ratio of their monthly expenditure is 5:4 . If each of them saves ₹2500 per month .Find their monthly incomes.​

Answer 1

$\sf\small\underline\purple{Let:}$

$\tt{\implies Their\: monthly\:_{(income)}=x}$

$\tt{\implies Their\: monthly\:_{(expenditure)}=y}$

$\sf\small\underline\purple{Given:}$

$\tt{\implies Their\: monthly\:_{(income)}=6:5}$

$\tt{\implies Their\: monthly\:_{(expenditure)}=5:4}$

$\tt{\implies Their\: monthly\:_{(savings\: each)}=2500}$

$\sf\small\underline\purple{To\: Find:}$

$\tt{\implies Their\: monthly\:_{(income)}=?}$

$\sf\small\underline\purple{Solution:}$

To calculate the monthly income of Amit and Atul, as per the question we have to set us equation then solve both equation by solving we get the value of x and y then we can easily calculate their income. In question, given that monthly income of Amit & Atul are in the ratio 6:5 .The ratio of their monthly expenditure is 5:4 . If each of them saves ₹2500 per month .Find their monthly incomes:-]

$\sf\small\green{\implies Amit\:_{(Income)}-Amit\:_{(expenditure)}=Amit\:_{(savings)}}$

$\tt{\implies 6x-5y=2500-----(i)}$

$\sf\small\green{\implies Atul\:_{(Income)}-Atul\:_{(expenditure)}=Atul\:_{(savings)}}$

$\tt{\implies 5x-4y=2500-----(ii)}$

• In eq (i) multiplying by 5 and in eq (ii) by 6:-]

$\tt{\implies 30x-25y=12500}$

$\tt{\implies 30x-24y=15000}$

• By solving we get here:-]

$\tt{\implies -y=-2500}$

$\tt{\implies y=2500}$

• Putting the value of y in eq (I)

$\tt{\implies 6x-5y=2500}$

$\tt{\implies 6x-5*2500=2500}$

$\tt{\implies 6x-12500=2500}$

$\tt{\implies 6x=2500+12500}$

$\tt{\implies 6x=15000}$

$\tt{\implies x=2500}$

$\sf\large{Hence,}$

$\tt{\implies Monthly\: income\:_{(Amit)}=6x}$

$\tt{\implies Monthly\: income\:_{(Amit)}=6*2500}$

$\bf{\implies Monthly\: income\:_{(Amit)}=Rs.15000}$

$\tt{\implies Monthly\: income\:_{(Atul)}=5x}$

$\tt{\implies Monthly\: income\:_{(Atul)}=5*2500}$

$\bf{\implies Monthly\: income\:_{(Atul)}=Rs.12500}$

Answer 2

Answer:

Correct Question :-

• The monthly income of Amit & Atul are in the ratio of 6 : 5. The ratio of their monthly expenditure is 5 : 4. If each of them saves Rs 2500 per month. Find their monthly incomes.

Given :-

• The monthly income of Amit & Atul are in the ratio of 6 : 5.
• The ratio of their monthly expenditure is 5 : 4.
• If each of them saves Rs 2500 per month.

To Find :-

• What is the monthly incomes.

Solution :-

$\mapsto$ Let's Amit income be Rs 6x

$\mapsto$ And, Atul income will be Rs 5x

Now, according to the question,

↪ $\sf \dfrac{6x - 2500}{5x - 2500} =\: \dfrac{5}{4}$

By doing cross multiplication we get,

↪ $\sf 5(5x - 2500) =\: 4(6x - 2500)$

↪ $\sf 25x - 12500 =\: 24x - 10000$

↪ $\sf 25x - 24x =\: - 10000 + 12500$

➨ $\sf\bold{\green{x =\: 2500}}$

Hence, the required income of Amit & Atul are :

➲ Monthly income of Amit :

↦ $\sf Rs\: 6x$

↦ $\sf Rs\: 6(2500)$

↦ $\sf Rs\: 6 \times 2500$

➠ $\sf\bold{\red{Rs\: 15000}}$

And,

➲ Monthly income of Atul :

↦ $\sf Rs\: 5x$

↦ $\sf Rs\: 5(2500)$

↦ $\sf Rs\: 5 \times 2500$

➠ $\sf\bold{\red{Rs\: 12500}}$

$\therefore$ The monthly income of Amit is Rs 15000 and the monthly income of Atul is Rs 12500 .