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.

 If 9 engines consume 24 metric tonnes of coal, when each is working 8 hours a day, how much coal will be required for 8 engines, each running 13 hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type?

Answer:

Explanation:

Let 3 engines of former type consume 1 unit in 1 hour.

Then, 4 engines of latter type consume 1 unit in 1 hour.

1 engine  of  former  type  consumes $\frac{1}{3}$ unit in 1 hour. 

1 engine of latter type consumes $\frac{1}{4}$ unit in 1 hour. 

Let the required consumption of coal be $x$ units.

Less engines, Less coal consumed                         (Direct Proportion)

More working hours, More coal consumed           (Direct Proportion)

Less rate of consumption, Less coal consumed  (Direct Proportion)

$\left\{\begin{array}{c}No.engines\quad\quad\quad\quad\quad\quad\quad\quad 9:8\\ Working\quad hours\quad\quad\quad\quad\quad\quad 8:13\\Rate\quad of\quad consumption\quad\quad\quad\frac{1}{3}:\frac{1}{4}\end{array}\right\}::24:x$

$\therefore \left(9\times 8\times\frac{1}{3}\times x\right)$ $=\left(8\times 13\times\frac{1}{4}\times 24\right)$

$\Leftrightarrow 3x=78$  $\Leftrightarrow x=26$

A contract is to be completed in 46 days and 117 men were set to work, each working 8 hours a day. After 33 days, $\frac{4}{7}$ of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day ?

Answer:

Explanation:

Remaining work $=1-\frac{4}{7}$ $=\frac{3}{7}$

Remaining period $=(46-33)$ days = 13 days.

Let the total men working at it be $x$.

Less work, Less men        (Direct Proportion)

Less days, More men        (Indirect Proportion)

More Hrs/Day, Less men (Indirect Proportion)

$\left\{\begin{array}{c}Wrok\quad\quad\quad \frac{4}{7}:\frac{3}{7}\\ Days\quad\quad\quad 13:33\\Hrs/Day\quad\quad9:8\end{array}\right\}::117:x$  

$\frac{4}{7}\times 13\times 9\times x$ $=\frac{3}{7}\times 33\times 8\times 117$

or $x=\left(\frac{3\times 33\times 8\times 117}{4\times 13\times 9}\right)$  $=198 $

Additional men to be employed $=(198-117)$ = 81.

A garrison of 3300 men had provisions for 32 days, when given at the rate of 850 gms per head. At the end of 7 days, a reinforcement arrives and it was found that the provisions will last 17 days more, when given at the rate of 825 gms per head. What is the strength of the reinforcement ?

Answer:

Explanation:

The problem becomes :

3300 men taking 850 gms per head have provisions for $(32-7)$ or 25 days. How many mei. taking 825 gms each have provisions for 17 days ?

Less ration per head, More men   (Indirect Proportion)

Less days, More men                       (Indirect Proportion) 

$\left\{\begin{array}{c}Ration\quad 825:850\\ Days\quad\quad 17:25\end{array}\right\}::3300:x$  

$825\times 17\times x$ $=850\times 25\times 3300$ or $x=\left(\frac{850\times 25\times 3300}{825\times 17}\right)$ = 5000

Strength of reinforcement $=(5500-3300)$ = 1700.

• Chain Rule - General Questions