Let me know the logic the solve these kind of problems

Question

One year ago, the ratio of Harsha's and Mandar's salaries was 3:5. The ratios of their individual salaries of last year and present year are 2:3 and 4:5 respectively. If their combined salary for the present year is Rs 86,000, find the present salary of Harsha

Answer 1

First off, try to write everything you know as an expression or equation.

Going in order through the problem I will let $H_1$ and $M_1$ be the salaries last year and $H_2$ and $M_2$ be the salaries this year: $$\frac{H_1}{M_1}=\frac{3}{5}\Rightarrow5H_1=3M_1$$ $$3H_1 = 2H_2, 5M_1 = 4M_2$$ $$H_1 = \frac{2}{3}H_2, M_1 = \frac{4}{5}M_2$$ $$H_2+M_2=86000$$

So, ideally we would like a second equation to go with that last sum so we can have two equations for two unknowns. Manipulating and substituting with the first two equations yields $$5\times\frac{2}{3}H_2=3\times\frac{4}{5}M_2\Rightarrow\frac{10}{3}H_2=\frac{12}{5}M_2$$ Now you have two equations with two unknowns for their current salaries. $$50H_2=36M_2$$ $$H_2+M_2=86000$$

Answer 2

Best thing to start with is assigning some variables to the unknowns, and setting up some equations with the given information. Let $h_1,h_2$ be the last year's and present salaries for Harsha, respectively, and let $m_1,m_2$ be the same for Mandar. With the given information, we know: $$\begin{cases}3h_1=5m_1\\2h_1=3h_2\\4m_1=5m_2\\m_2+h_2=86000\end{cases}$$ There are enough equations now to substitute, and rearrange to have an equation only involving $m_2$, which gives Mandar's present year's salary.

Answer 3

Just retranscript the problem statement

1. $\dfrac{H_0}{M_0}=\dfrac35$

2. $\dfrac{H_0}{H_1}=\dfrac23,\dfrac{M_0}{M_1}=\dfrac45$

3. $H_1+M_1=86000$

This is a system of four equations in four unknowns, which can be put in a linear form.

For convenience, eliminate $H_0$ and $M_0$ with $$H_0=\frac23H_1,M_0=\frac45M_1$$ and the system becomes

$$\begin{cases}5\dfrac23H_1-3\dfrac45M_1=0,\\H_1+M_1=86000\end{cases}$$

which should raise no difficulty.