FACTS  AND  FORMULAE  FOR  CHAIN  RULE  QUESTIONS

 

 

1. Direct Proportion: Two quantities are said to be directly proportional, if on the increase (or decrease) of the one, the other increases (or decreases) to the same extent.

Ex. 1. Cost is directly proportional to the number of articles. (More Articles, More Cost)

Ex. 2. Work done is directly proportional to the number of men working on it (More Men, More Work)

 

2. Indirect Proportion: Two quantities are said to be indirectly proportional,if on the increase of the one, the other decreases to the same extent and vice-versa.

Ex. 1. The time taken by a car in covering a certain distance is inversely proportional to the speed of the car. (More speed, Less is the time taken to cover a distance)

Ex. 2. Time taken to finish a work is inversely proportional to the num of persons working at it. (More persons, Less is the time taken to finish a job)

Q:

2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the same in 11 days. Then, 8 men and 6 boys can do three times the amount of this work in 

A) 18 days B) 21 days
C) 24 days D) 30 days
 
Answer & Explanation Answer: B) 21 days

Explanation:

\inline \fn_jvn (2\times 14) men +(7\times 14)boys=(3\times 11)men+(8\times 11)boys

\inline \fn_jvn \Leftrightarrow  5 men= 10 boys  \inline \fn_jvn \Leftrightarrow  1man= 2 boys

\inline \fn_jvn \therefore  (2 men+ 7 boys) = (2 x 2 +7) boys = 11 boys

     ( 8 men + 6 boys) = (8 x 2 +6) boys = 22 boys.

Let the required  number of days be x.

More boys , Less days     (Indirect proportion)

More work , More days    (Direct proportion)

\inline \fn_jvn \left.\begin{matrix} Boys\: 22:11\\ Work\: 1:3 \end{matrix}\right\}::14:x  

\inline \fn_jvn \therefore \: \: (22\times 1\times x)=(11\times 3\times 14)   \inline \fn_jvn \Leftrightarrow  \inline \fn_jvn x= \frac{462}{22}=21

Hence, the required number of days = 21

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19 11116
Q:

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?

A) 75 B) 82
C) 100 D) 110
 
Answer & Explanation Answer: D) 110

Explanation:

Originally let there be x men.

Less men, More days     (Indirect Proportion)

\inline \fn_jvn \therefore  (x-10) : x  :: 100 :110   \inline \fn_jvn \Leftrightarrow  \inline \fn_jvn (x-10)\times 110=x\times 100  \inline \fn_jvn \Leftrightarrow  10x= 1100    \inline \fn_jvn \Leftrightarrow  x= 110

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25 10973
Q:

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

A) 46 B) 47
C) 48 D) 49
 
Answer & Explanation Answer: D) 49

Explanation:

Let the required length be x meters

More men, More length built     (Direct proportion)

Less days, Less length built      (Direct Proportion)

\inline \fn_jvn \left.\begin{matrix} Men\: \: \: 20:35\\ Days\: 6:3 \end{matrix}\right\}::56:x

\inline \fn_jvn \therefore  (20 x 6 x X)=(35 x 3 x 56) \inline \fn_jvn \Leftrightarrow  \inline \fn_jvn x=\frac{35\times 3\times 56}{120} =49

Hence, the required length is 49 m.

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33 10145
Q:

3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

A) 9 B) 10
C) 11 D) 12
 
Answer & Explanation Answer: D) 12

Explanation:

Let the required no of working hours per day be x.

More pumps , Less working hours per day  (Indirect Proportion)

Less days, More working hours per day      (Indirect Proportion)

\inline \fn_jvn \left.\begin{matrix} pumps\: 4:3\\ Days\; \; \; \; 1:2 \end{matrix}\right\}::8:x

\inline \fn_jvn \therefore  \inline \fn_jvn 4\times 1\times x= 3\times 2\times 8   \inline \fn_jvn \Leftrightarrow  X= \inline \fn_jvn \frac{3\times 2\times 8}{4}   \inline \fn_jvn \Leftrightarrow  x=12

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15 9363
Q:

If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?

A) 1 B) 3
C) 7 D) 14
 
Answer & Explanation Answer: C) 7

Explanation:

Let the required number days be x.

Less spiders, More days (Indirect Proportion)

Less webs, Less days (Direct Proportion)

\inline {\color{Blue} \left.\begin{matrix} spiders &1:7 \\ webs & 7:1 \end{matrix}\right\}::7:x}

\inline {\color{Blue} \therefore } 1 x 7 x x = 7 x 1 x 7

=> x= 7

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21 9007