Chain Rule Questions and Answers

Answer: D

Reduce to a single weaver before scaling up. Four weavers making 4 mats in 4 days means

\[ 1 \text{ weaver} \rightarrow 1 \text{ mat in } 4 \text{ days} \]

Output is proportional to both the number of weavers and the time given, so

\[ \text{mats} = 8 \text{ weavers} \times \frac{8 \text{ days}}{4 \text{ days per mat}} = 8 \times 2 = 16 \]

The intuitive answer of 8 comes from doubling only one of the two factors. Both the workforce and the time double here, so the output goes up fourfold.

Answer: C

Read the rate per cow rather than for the herd. If 40 cows finish 40 bags in 40 days, then in those same 40 days

\[ \text{each cow eats } \frac{40 \text{ bags}}{40 \text{ cows}} = 1 \text{ bag} \]

so one cow takes 40 days for one bag.

The number of cows never enters the answer: each is eating alongside the others, not sharing a single bag. Dividing 40 by 40 to get 1 day is the classic slip, and it would mean the herd polished off 40 bags in a single day.

Answer: D

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)

 Pumps4 : 3Days1 : 2⋮⋮ 8:x

=> (4 * 1 * x) = (3 * 2 * 8)

=> x=12

Answer: B

Count the man-days actually worked.

\[ 100 \times 35 + 200 \times 5 = 3500 + 1000 = 4500 \]

With only the original 100 men:

\[ \frac{4500}{100} = 45 \text{ days} \]

\[ 45 - 40 = 5 \text{ days behind schedule} \]

Answer: B

Let the required number of days be x.

Less persons, More days (Indirect Proportion)

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

Persons30:39Working hours/day6:5⋮⋮ 12:x

=> 30 * 6 * x = 39 * 5 * 12 

=> x= 13

Answer: C

Let the required number days be x.

Less spiders, More days (Indirect Proportion)

Less webs, Less days (Direct Proportion)

 Spiders1:7Webs7:1⋮⋮ 7:x 

=> 1 * 7 * x = 7 * 1 * 7 

=> x= 7

Answer: B

The meal is one fixed quantity, described two ways, so the two descriptions are equivalent:

\[ 120 \text{ men} \equiv 200 \text{ children} \]

After 150 children have eaten, what is left would feed \( 200 - 150 = 50 \) children. Converting that share to men:

\[ 50 \text{ children} \times \frac{120 \text{ men}}{200 \text{ children}} = 30 \text{ men} \]

The step that matters is doing the subtraction in children and converting only at the end; converting first and then subtracting mixes the two units.

Answer: B

Earlier dimensions of the wall = 100 × 3 × 0.30.
New dimensions = L × 1.5 × 0.3.
∴ As men, women and children are given to be equally efficient, so in the first case, the total number of persons is 100 (i.e. 30 + 20 + 50) and the same in the second case is 75 (15 + 25 + 35).
Length of wall = L = (75x100) x (2x9) x (15x20) x (100 x 3 x 3 x 0.3)/(1.5 x 0.3) ⇒ L = 25 m.

Answer: D

The price is directly proportional to the number of toys, so scale by the ratio:

\[ \text{price of }5 = 264.37 \times \frac{5}{6} = 220.31 \]

which is about Rs. 220.

For an approximation the arithmetic can be done in the head: 6 toys at roughly Rs. 264 means about Rs. 44 each, and \( 5 \times 44 = 220 \).

Answer: B

Divide the length required by the rate of weaving:

\[ t = \frac{25}{0.128} = 195.3 \text{ seconds} \]

so about 195 seconds.

A quick check on the size of the answer: at roughly 0.128 m per second the loom weaves a little under 8 metres per minute, so 25 metres must take somewhat over three minutes - which rules out both 250 and 844 immediately.