Question

If the ratio of incomes of A and B is 2:1 and the ratio of their spends is 5:2. If each saves Rs 300 per month.find the income of B?


This is the question of linear equation of two variable (Problem sum)​

Answer 1

Given :

• Ratio of incomes of A and B is 2:1
• Ratio of their spends is 5:2
• Each saves Rs. 300 per month.

To Find :

• The income of B.

Solution :

Let,

• Ratio of incomes of A and B be 2x and 1y
• Ratio of spends of A and B be 5x and 2y

$\dashrightarrow \ \: \sf \: 2x - 1y = Rs. \: 300 \: \: . \: \: . \: \: .(eq. \: \bf \: 1 \sf)$

$\dashrightarrow \ \: \sf \: 5x - 2y = Rs. \: 300 \: \: . \: \: . \: \: .(eq. \: \bf \: 2 \sf)$

Now multiply equation (1) by 2 and equation (2) by 5 since A's income is 2x and its spends is 5x.

$\implies \tt \: 4x - 2y = Rs. \: 600 \: \: . \: \: . \: \: .(eq. \: \bf \: 3 \sf)$

$\implies \tt \: 10x - 5y = Rs. \: 1500 \: \: . \: \: . \: \: .(eq. \: \bf \: 4 \sf)$

$\implies \tt \: \: 1500 - 600 \\ \\ \implies \underline{ \bf{x = 900}}$

Now, according to the question let's calculate the income of B.

Given that, the ratio of A and B is 2x and 1x.

Income of A :-

$\implies \: \bf \: 2x = 2 \times 900 \\ \\ \implies \underline{ \boxed{ \pink{ \bf{1800}}}}$

Income of B :-

$\implies \: \bf \: 1x =1 \times 900 \\ \\ \implies \underline{ \boxed{ \purple{ \bf{900}}}}$

$\therefore \: \green{\tt{the \: income \: of \: B \: is \: 900 \: rupees}}$ .