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

Let:

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

(income)

=x

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

(expenditure)

=y

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

Given:

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

(income)

=6:5

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

(expenditure)

=5:4

\tt{\implies Their\: monthly\:_{(SAVINGS\: each)}=2500}⟹Theirmonthly

(savingseach)

=2500

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

ToFind:

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

(income)

=?

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

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)}}⟹Amit

(Income)

−Amit

(expenditure)

=Amit

(savings)

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

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

(Income)

−Atul

(expenditure)

=Atul

(savings)

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

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

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

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

By solving we get here:-]

\tt{\implies -y=-2500}⟹−y=−2500

\tt{\implies y=2500}⟹y=2500

Putting the value of y in eq (I)

\tt{\implies 6x-5y=2500}⟹6x−5y=2500

\tt{\implies 6x-5*2500=2500}⟹6x−5∗2500=2500

\tt{\implies 6x-12500=2500}⟹6x−12500=2500

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

\tt{\implies 6x=15000}⟹6x=15000

\tt{\implies x=2500}⟹x=2500

\sf\large{Hence,}Hence,

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

(Amit)

=6x

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

(Amit)

=6∗2500

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

(Amit)

=Rs.15000

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

(Atul)

=5x

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

(Atul)

=5∗2500

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

(Atul)

=Rs.12500