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 15 toys cost Rs. 234, what do 35 toys cost ?

Answer:

Explanation:

Let the required cost be Rs. $x$. Then,

More toys, More cost (Direct Proportion)

$\therefore 15:35::234:x$

$(15\times x)=(35\times 234)$   

$x=\frac{35\times 234}{15}$ $= 546$.

Hence, the cost of 35 toys is Rs. 546.

If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it ?

Answer:

Explanation:

Let the required number of hours be $x$. Then,

Less men, More hours (Indirect Proportion)

$\therefore 15:36 :: 25:x$

$(15\times x)=(36\times 25)$   

$\Leftrightarrow x=\frac{36\times 25}{15}$ $= 60$.

Hence, 15 men can do it in 60 hours.

If the wages of 6 men for 15 days be Rs. 2100, then find the wages of 9 men for 12 days.

Answer:

Explanation:

Let the required wages be Rs. $x$.

More men, More wages (Direct Proportion)

Less days, Less wages  (Direct Proportion)

$\left\{\begin{array}{c}Men\quad\quad 6:9\\ Days\quad 15:12\end{array}\right\}::2100:x$

$\therefore(6\times 15\times x)$ $=(9\times 12\times 2100)$

$\Leftrightarrow x=\frac{9\times 12\times 2100}{6\times 15}$ $=2520.$

Hence, the required wages are Rs. 2520.

If 20 men can build a wall 56 metres long in 6 days, what length of a similar wall can be built by 35 men in 3 days ?

Answer:

Explanation:

Let the required length be $x$ metres.

More men, More length built  (Direct Proportion)  

Less days, Less length built   (Direct Proportion)

$\left\{\begin{array}{c}Men\quad 20:35\\ Days\quad 6:3\end{array}\right\}::56:x$

$\therefore(20\times 6\times x)=(35\times 3\times 56)$

$\Leftrightarrow\frac{35\times 3\times 56}{120}$ $= 49$.

Hence, the required length is 49 m.

If 15 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day ?

Answer:

Explanation:

Let the required number of days be $x$

More men, Less days               (Indirect Proportion)

Less hours per day, More days   (Indirect Proportion)

$\left\{\begin{array}{c}Men\quad\quad\quad 18:15\\ Hours/Day\quad 8:9\end{array}\right\}::16:x$

$ \therefore(18\times 8\times x)=(15\times 9\times 16)$

$\Leftrightarrow x=\frac{15\times 144}{144}$ $=15$

Hence, required number of days = 15.

• Chain Rule - General Questions