Arithmetic aptitude :: Chain Rule :: General Questions

• Chain Rule - General Questions
• Chain Rule - Important Formulas and Facts

Directly Proportional:
If two amounts are said to be in directly proportional then, as one amount increases another amount increases at the same extent.

e.g. Your earnings is directly proportional to your working hours.

• Work more hours, get more pay; (direct proportion).

Inversely Proportional:
when one amount decreases at the same extent that the other increases.

e.g Speed and travel time are Inversely Proportional

• As speed increases, travel time decreases
• And as speed decreases, travel time increases

Note: To solve problems by chain rule, you should compare every item with the term to be found out.

A contractor undertook to do a certain piece of work in 9 days. He employed certain number of men, but 6 of them being absent from the very first day, the rest could finish the work in 15 days. The number of men originally employed were :

Answer:

Explanation:

Let there be $x$ men at the beginning.

Less men, More days (Indirect Proportion)

$15:9::x:(x-6)$ $\Leftrightarrow 15(x-6)=9x$

$\Leftrightarrow 6x=90$ $\Leftrightarrow x=15$

12 men and 18 boys, working $7\frac{1}{2}$ hours a day, can do a piece of work in 60 days. If a man works equal to 2 boys, then how many boys will be required to help 21 men to do twice the work in 50 days, working 9 hours a day ?

Answer:

Explanation:

$1$ man = $2$ boys  $\Rightarrow$ ($12$ men + $18$ boys) $=(12\times 2+18)$ boys = 42 boys

Let required number of boys $= x$.

$21$ men + $x$ boys $=(21\times 2+x)$ boys $=(42+x)$ boys

Less days, More boys (Indirect Proportion)

More hrs per day, Less boys (Indirect Proportion)

$\left\{\begin{array}{c}Days\quad\quad\quad 50:60\\ Hours/Day\quad 9:\frac{15}{2}\\Work\quad\quad\quad\quad 1:2\end{array}\right\}::42:(42+x)$

$\therefore [50\times 9\times 1\times(42+x)]$ $=\left(60\times \frac{15}{2}\times 2\times 42\right)$

$\Leftrightarrow (42+x)$ $=\frac{37800}{450}$

$\Leftrightarrow 42+x=84$ 

$\Leftrightarrow x=42$.

A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the beginning and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished ?

Answer:

Explanation:

$[(100\times 35)+(200\times 5)]$ men can finish the work in $1$ day.

$\therefore 4500$ men can finish the work in 1 day.

$100$ men can finish it in $\frac{4500}{100}$ = 45 days.

This is 5 days behind schedule.

If 3 men or 6 boys can do a piece of work in 10 days, working 7 hours a day; how many days will it take to compete a piece of work twice as large with 6 men and 2 boys working together for 8 hours a day ?

Answer:

Explanation:

3 men = 6 boys = (6 men + 2 boys) = 14 boys.

More work, More days (Direct Proportion)

More boys, Less days (Indirect Proportion)

More hours per day, Less days      (Indirect Proportion)

$\left\{\begin{array}{c}Work\quad\quad\quad\quad\quad\quad 1:2\\ Boys\quad\quad\quad\quad\quad\quad 14:6\\Hours/Day\quad\quad\quad\quad 8:7\end{array}\right\}::10:x$

$\therefore (1\times 14\times 8\times x)$ $=(2\times 6\times 7\times 10)$  

$\Leftrightarrow x=\frac{840}{112}$ $=7\frac{1}{2}$

 A contractor employed 30 men to do a piece of work in 38 days. After 25 days, he employed 5 men more and the work was finished one day earlier. How many days he would have been behind, if he had not employed additional men ?

Answer:

Explanation:

After 25 days, 35 men complete the work in 12 days.

Thus, 35 men can finish the remaining work in 12 days.

$\therefore$ 30 men can do it in $\frac{12\times 35}{30}$ = 14 days, which is 1 day behind.

• Chain Rule - General Questions