# Thread: basic but needs brains

1. ## basic but needs brains

1. a worker suffers a 20 percent cut in wages. he regains his original pay buy obtaining a rise of?

(its not 20...!)

2. m men can do a job in d days, then the number of days in which m+r men would do the same?

3. a boy walks from his home to school at 6kmph . walks back at 2 kmph. avg. speed=?

1. a worker suffers a 20 percent cut in wages. he regains his original pay buy obtaining a rise of?

(its not 20...!)
After the cut he earns 80% of his original income. To rise these 80% to a 100% again he has to add 20%. The percentage is $\displaystyle p=\dfrac{20}{80} \cdot 100\% = 25\%$

...

3. a boy walks from his home to school at 6kmph . walks back at 2 kmph. avg. speed=?
Let s denote the distance from home to school. Then the first elapsed time is:

$\displaystyle t_1 = \dfrac s{6\ \frac{km}{h}}$ and

$\displaystyle t_2 = \dfrac s{2\ \frac{km}{h}}$

The boy walks the distance twice. Then the average speed is:

$\displaystyle v=\dfrac{2s}{t_1+t_2}=\dfrac{2s}{\dfrac s{6\ \frac{km}{h}} + \dfrac s{2\ \frac{km}{h}}} = \dfrac{2s}{\dfrac23 s \ \frac{km}{h}} = 3 \ \frac{km}{h}$

3. thnx. just one more.........

4. Well? We are waiting impatiently!

5. Originally Posted by HallsofIvy
Well? We are waiting impatiently!
Probably adhyeta is refering to the question #2.

But I can't answer this question because I don't know what these variables m, r mean ...

6. Originally Posted by earboth
After the cut he earns 80% of his original income. To rise these 80% to a 100% again he has to add 20%. The percentage is $\displaystyle p=\dfrac{20}{80} \cdot 100\% = 25\%$

...

Let s denote the distance from home to school. Then the first elapsed time is:

$\displaystyle t_1 = \dfrac s{6\ \frac{km}{h}}$ and

$\displaystyle t_2 = \dfrac s{2\ \frac{km}{h}}$

The boy walks the distance twice. Then the average speed is:

$\displaystyle v=\dfrac{2s}{t_1+t_2}=\dfrac{2s}{\dfrac s{6\ \frac{km}{h}} + \dfrac s{2\ \frac{km}{h}}} = \dfrac{2s}{\dfrac23 s \ \frac{km}{h}} = 3 \ \frac{km}{h}$
I'd do question 1 differently.

Let $\displaystyle p_{o}$ represent his original salary and $\displaystyle p_n$ represent the new.

From our information, he has received a 20% pay cut, so he is receiving 80% of what he was originally getting.

$\displaystyle p_n = 80\%\textrm{ of }p_o$

$\displaystyle = \frac{80}{100}\times p_o$

$\displaystyle = \frac{4}{5}p_o$.

Therefore to get back to the original salary

$\displaystyle p_o = \frac{5}{4} p_n$

$\displaystyle = \frac{125}{100} \times p_n$

$\displaystyle = 125\%\textrm{ of }p_n$.

So he would need a 25% pay increase to get back to his original salary.

7. Originally Posted by earboth
Probably adhyeta is refering to the question #2.

But I can't answer this question because I don't know what these variables m, r mean ...

a typo.
the questions said-if m men can do a job in d days, then the days reqd for m+r men=?

a typo.
the questions said-if m men can do a job in d days, then the days reqd for m+r men=?
$\displaystyle \begin{array}{lcr}m\ men&\rightarrow\ need \ \rightarrow& \ d\ days \\ 1\ man&\rightarrow\ needs \ \rightarrow& \ m \cdot d\ days \\ m+r\ men&\rightarrow\ need \ \rightarrow &\ \dfrac{m\cdot d}{m+r}\ days \end{array}$

9. lol. thnx earboth. i was doing m men-d days, then 1 man-d/m days.