Question

Suresh and Ramesh together invested $1,44,000$ rupees in the ratio $4:5$ and bought a plot of land. After some years they sold it at a profit of $20\% $. What is the profit each of them got?

Answer 1

Hint: In this question we need to find the profit amount of both. For that we are going to find the invested amount of both and also the profit amount using profit percentage formulas used. Before that we need to know about cost price and selling price commonly known as C.P. and S.P. respectively. The things we buy are called cost price and the things we sell are selling price.

Formula used: \[{\text{profit}}\% = \dfrac{{{\text{profit}}}}{{C.P}} \times 100\]
\[{\text{profit}} = \dfrac{{{\text{profit}}\% \times C.P}}{{100}}\]
\[{\text{profit = S}}{\text{.P - C}}{\text{.P}}\]
\[{\text{S}}{\text{.P = C}}{\text{.P + profit}}\]

Complete step-by-step answer:
Let the amount invested by Suresh = \[4x\;\; - - - - - - - - - - - - - - - - - \left( 1 \right)\]
Let the amount invested by Ramesh = \[5x - - - - - - - - - - - - - - - - - \left( 2 \right)\]
Let the Cost Price (c.p.) \[ = 1,44,000\]
First, we need to find Individual invested amount of both, for that we need to add ratio of both and divide them with their total invested amount, we get
Total amount invested \[ = 1,44,000\]
\[ \Rightarrow 4x{\text{ }} + {\text{ }}5x{\text{ }} = {\text{ }}1,44,000\]
\[ \Rightarrow 9x{\text{ }} = {\text{ }}1,44,000\]
\[ \Rightarrow x = \dfrac{{1,44,000}}{9}\]
Dividing \[1,44,000\] by \[9\], we get,
\[x{\text{ }} = {\text{ }}16,000{\text{ }} - - - - - - - {\text{ }}\left( 3 \right)\]
Now, we find the Cost Price of both by substituting equation (3) value in equation (1) & (2), we get
Cost Price of Suresh \[ = {\text{ }}4{\text{ }} \times {\text{ }}16,000\]
Cost Price of Suresh \[ = {\text{ }}64,000\]
Cost Price of Ramesh \[ = {\text{ }}5{\text{ }} \times {\text{ }}16,000\]
Cost Price of Ramesh \[ = 80,000\]
Now, we find the profit amount for that we need to use formula mentioned in formula used,
\[{\text{profit}} = \dfrac{{1,44,000 \times 20}}{{100}}\]
Simplifying we get,
\[{\text{profit}} = \dfrac{{28,80,000}}{{100}}\]
Now, dividing numerator and denominator by 100, we get
\[\therefore {\text{profit}} = 28,800\]
Now we need to find selling price for that we need to use formula mentioned in formula used
\[ \Rightarrow S.P = 1,44,000 + 28,800\]
\[\therefore S.P = 1,72,800\]
Now, we can find the profit amount of both for that like previous we need to add ratio of both and then find profit amount of both
\[ \Rightarrow 4x{\text{ }} + {\text{ }}5x{\text{ }} = {\text{ }}1,72,800\]
Adding the terms we get,
\[ \Rightarrow 9x{\text{ }} = {\text{ }}1,72,800\]
Let solve this for \[x\],
\[ \Rightarrow x = \dfrac{{1,72,800}}{9}\]
\[\therefore x = 19,200 - - - - - - - - - - \left( 4 \right)\]
Now, we find the Selling Price of both separately, we need to substitute value equation (4) in equation (1) & (2), we get,
Selling Price of Suresh = \[4{\text{ }} \times {\text{ }}19,200\]
Selling Price of Suresh \[ = {\text{ }}76,800\]
Selling Price of Ramesh \[ = {\text{ }}5{\text{ }} \times {\text{ }}19,200\]
Selling Price of Ramesh \[ = {\text{ }}96,000\]
Now, we find the profit amount of both separately by subtracting Selling Price from Cost Price of both
\[{\text{Profit of Suresh = Selling Price of Suresh - Cost Price of Suresh}}\]
\[ \Rightarrow {\text{ }}76,800{\text{ }}-{\text{ }}64,000\]
Profit of Suresh \[ = {\text{ }}12,800\]
\[{\text{Profit of Ramesh = Selling Price of Ramesh - Cost Price of Ramesh}}\]
\[ \Rightarrow {\text{ }}96,000{\text{ }}-{\text{ }}80,000\]
Profit of Ramesh \[ = {\text{ }}16,000\]
$\therefore $ Thus the profit amount of Suresh and Ramesh are \[12,800\] and \[16,000\].

Note: This type of problem needs attention on question it may give many leads to you. This problem comes under the profit and loss topic and we need to be used with formulas on it. It is basic day to day life problems it also comes under life mathematics.