The incomes of A and B are in the ratio 3:5 and their expenditures are

1.	The incomes of A and B are in the ratio 3:5 and their expenditures are in the ratio 2:3 . If A save Rs.8000 and B saves Rs.15000, then the income of A is *
Answer» $\large\underline\pink{Given:-}$ RATIO of income of A and B ⇢ 3 : 5 Ratio of their expenditures ⇢ 2 : 3 A saver Rs. 8000 and B savers Rs. 15000 $\large\underline\pink{To find:-}$ find it's income of A ...? $\large\underline\pink{Solutions:-}$ LET the income of A be 3x and B be 5x. Let the expenditure of A be 2y and B be 3y. ✰ Then, SAVING of A is Rs. 8000 and Saving of B is Rs. 15000. »★ We have $\: \: \: \: \: \orange{\star \: \: \: {3x} \: - \: {2y} \: \: = \: \: {1800} \: \: \: \: \: \: \: ....{(i)}.}$ $\: \: \: \: \: \orange{\star \: \: \: {5x} \: - \: {3y} \: \: = \: \: {15000} \: \: \: \: \: \: \: ....{(<klux>II</klux>)}.}$ »★ Multiplying Eq. (i) by 3. and Eq. (ii) by 2. $\: \: \: \: \: \orange{\star \: \: \: {9x} \: - \: {6y} \: \: = \: \: {24000} \: \: \: \: \: \: \: ....{(iii)}.}$ $\: \: \: \: \: \orange{\star \: \: \: {10x} \: - \: {6y} \: \: = \: \: {30000} \: \: \: \: \: \: \: ....{(iv)}.}$ »★ Now, Subtracting Eq. (iii) and Eq. (iv) ${9x} \: - \: {6y} \: \: = \: \: {24000} \\ {10x} \: - \: {6y} \: \: = \: \: {30000} \\ \underline{- \: \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: = \: \: \: \: + \: \: \: \: \: \: \: \: } \\ {x} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: {6000}$ »★ So, The income of A. $\: \: \: \: \: \leadsto \: \: \orange{{3x} \: \: = \: \: {3} \: \times \: {6000}}$ $\: \: \: \: \: \leadsto\orange{\: \: {3x} \: \: = \: \: {18000}}$ $\: \: \: \: \: \pink{\star \: \: \: Hence, }$ $\: \: \: \: \: \therefore \: \: the \: \: income \: \: of \: \: A \: \: is \: \: {18000}$ $\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star$

The incomes of A and B are in the ratio 3:5 and their expenditures are in the ratio 2:3 . If A save Rs.8000 and B saves Rs.15000, then the income of A is *

Answer»

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

RATIO of income of A and B ⇢ 3 : 5
Ratio of their expenditures ⇢ 2 : 3
A saver Rs. 8000 and B savers Rs. 15000

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

find it's income of A ...?

$\large\underline\pink{Solutions:-}$

LET the income of A be 3x and B be 5x.
Let the expenditure of A be 2y and B be 3y.

✰ Then, SAVING of A is Rs. 8000 and Saving of B is Rs. 15000.

»★ We have

$\: \: \: \: \: \orange{\star \: \: \: {3x} \: - \: {2y} \: \: = \: \: {1800} \: \: \: \: \: \: \: ....{(i)}.}$

$\: \: \: \: \: \orange{\star \: \: \: {5x} \: - \: {3y} \: \: = \: \: {15000} \: \: \: \: \: \: \: ....{(<klux>II</klux>)}.}$

»★ Multiplying Eq. (i) by 3. and Eq. (ii) by 2.

$\: \: \: \: \: \orange{\star \: \: \: {9x} \: - \: {6y} \: \: = \: \: {24000} \: \: \: \: \: \: \: ....{(iii)}.}$

$\: \: \: \: \: \orange{\star \: \: \: {10x} \: - \: {6y} \: \: = \: \: {30000} \: \: \: \: \: \: \: ....{(iv)}.}$

»★ Now, Subtracting Eq. (iii) and Eq. (iv)

${9x} \: - \: {6y} \: \: = \: \: {24000} \\ {10x} \: - \: {6y} \: \: = \: \: {30000} \\ \underline{- \: \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: = \: \: \: \: + \: \: \: \: \: \: \: \: } \\ {x} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: {6000}$