Question

Annual expenses of A and B are in the ratio 7 : 3. Their annual savings are in the ratio 2 : 1. Find the annual savings of B, if the annual incomes of A and B are Rs. 11,000 and Rs. 5000 respectively​

Answer 1

AnswEr:-

Annual savings of B = Rs.2000

$\rule{200}{1}$

Solution:-

Let the annual expenses of A & B be 7m & 3m respectively.

And,let the annual savings of A & B be 2n & n respectively.

As we know,

→Total income = Total expense + Total savings

Case 1:-

As annual income of A = Rs.11000 and annual income of B = Rs.5000

⇒ 7m + 2n = 11000 - - (Eq.1)

⇒ 3m + n = 5000 - - (Eq.2)

Now multiplying (Eq.1) by 3 & (Eq.2) by 7 and substract (Eq.2) from (Eq.1)

⇒(21m + 6n) - (21m + 7n)= 33000 - 35000

⇒ 21m + 6n - 21m - 7n = -2000

⇒ -n = -2000

⇒ n = 2000

★ Annual savings of B:-

⇒ Annual savings of B = n

⇒ Annual savings of B = Rs.2000

Therefore,

Annual savings of B = Rs.2000 .

Answer 2

Answer:

$\boxed{\setlength{\unitlength}{.8mm}\begin{picture}(40,22)\thicklines\put(25,15){\vector(1,-1){10}}\put(15,15){\vector(-1,-1){10}}\put(9,18){\sf\large\underline{\bigstar \:Income}}\put(0,1){\sf{Expense}}\put(18,1){+}\put(25,1){\sf{Saving}}\end{picture}}\quad\boxed{\begin{minipage}{5.2 cm}\qquad\qquad\quad\underline{\tt{For A :}}\qquad\underline{\tt{For B :}}\\\\\sf Income = Rs. 11000\quad Rs. 5000 \\Expenses = 7\qquad\quad:\quad\qquad3\\Savings = 2\qquad\quad\:\::\:\quad\qquad1\end{minipage}}$

$\rule{120}{1}$

Let the Savings of A & B be 2x and x.

$\underline{\bigstar\:\:\textsf{According to the Question :}}$

$:\implies\tt \dfrac{A(Income-Saving)}{B(Income-Saving)}=\dfrac{A's\: Expense}{B's\: Expense}\\\\\\:\implies\tt \dfrac{11000 - 2x}{5000 - x} = \dfrac{7}{3}\\\\{\scriptsize\qquad\bf{\dag}\:\:\textsf{By Cross Multiplication.}}\\\\:\implies\tt 3(11000 - 2x) = 7(5000 - x)\\\\\\:\implies\tt 33000 - 6x = 35000 - 7x\\\\\\:\implies\tt 7x - 6x = 35000 - 33000\\\\\\:\implies\tt x = 2000$

$\rule{180}{2}$

$\underline{\bigstar\:\:\textsf{Savings :}}$

$\bullet\:\:\textsf{A = 2x = 2(2000) \textbf{Rs. 4,000}}\\\bullet\:\:\textsf{B = x = \textbf{Rs. 2,000}}$

⠀

$\therefore\:\underline{\textsf{Annual Saving of B will be \textbf{Rs. 2,000}}}.$