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 garrison of 500 men had provisions for 27 days. After 3 days a reinforcement of 300 men arrived. For how many more days will the remaining food last now ?

Answer:

Explanation:

Let the remaining food will last for $x$ days.

500 men had provisions for $(27-3)$ = 24 days.

$(500 + 300)$ men had provisions for $x$ days.

More men, Less days  (Indirect Proportion)

$\therefore$ $800 :500$ $::24:x$   $\Leftrightarrow (800\times x)$ $=(500\times 24)$

$\Leftrightarrow \frac{500\times 24}{800}=15$

15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take, if 3 women do as much work as 2 men ?

Answer:

Explanation:

3 women = 2 men. So, 21 women = 14 men.

Less men. More days (Indirect Proportion)

Less hours per day, More days (Indirect Proportion)

$\left\{\begin{array}{c}Men\quad\quad\quad 14:5\\ Hours/Day\quad 6:8\end{array}\right\}::21:x$

$(14\times 6\times x)$ $=(15\times 8\times 21)$  $\Leftrightarrow x=\frac{15\times 8\times 21}{14\times 6}$ = 30.

Required number of days = 30.

Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in :

Answer:

Explanation:

Let $x$ men can do the work in $12$ days and the required number of days be $z$.

More men, Less days (Indirect Proportion)

Less work, Less days (Direct Proportion)

$\left\{\begin{array}{c}Men\quad 2x:x\\ Work\quad 1:\frac{1}{2}\end{array}\right\}::12:z$

$\therefore (2x\times 1\times z)$ $= \left(x\times\frac{1}{2}\times 12\right)$  

$2xz=6x$  $z =3$

 A certain number of men can finish a piece of work in 100 days. If, there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally ?

Answer:

Explanation:

Originally, let there be $x$ men.

Less men, More days (Indirect Proportion)

$\therefore$ $(x-10):x::100:110$

$ (x-10)\times 110$ $=x\times 100$ $\Leftrightarrow 10x=1100$ $\Leftrightarrow x= 110$.

If a certain number of workmen can do a piece of work in 25 hours, in how many hours will another set of an equal number of men, do a piece of work, twice as great, supposing that 2 men of the first set can do as much work in an hour, as 3 men of the second set do in an hour ?

Answer:

Explanation:

Let the required number of hours be $x$.

Speeds of working of first and second type of men are $\frac{1}{2}$ and $\frac{1}{3} $

More work, More time (Direct Proportion)

Less speed, More time (Indirect Proportion)

$\left\{\begin{array}{c}Work\quad 1:2\\ Speed\quad \frac{1}{3}:\frac{1}{2}\end{array}\right\}::25:x$

$\therefore\left(1\times\frac{1}{3}\times x\right)$ $=\left(2\times\frac{1}{2}\times 25\right)$

$\Leftrightarrow x=75$

• Chain Rule - General Questions