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?
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
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A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the begining and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?
Answer: B
Count the man-days actually worked.
\[ 100 \times 35 + 200 \times 5 = 3500 + 1000 = 4500 \]
With only the original 100 men:
\[ \frac{4500}{100} = 45 \text{ days} \]
\[ 45 - 40 = 5 \text{ days behind schedule} \]
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39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
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
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If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?
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
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In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be created to with the remaining meal?
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.
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A 100 m long 3 m high and 30 cm wide wall is built by 30 men, 20 women and 50 children working 9 hours a day in 20 days. How long a wall 1.5 m high 30 cm wide can be built by 15 men, 25 women and 35 children working 2 hour a day in 15 days (given men, women and children are equally efficient)?
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.
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If the price of 6 toys is Rs. 264.37, what will be the approximate price of 5 toys?
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 \( 5 \times 44 = 220 \).
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An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metres of cloth?
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.
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36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ?
Answer: A
Less Men, means more Days {Indirect Proportion}
Let the number of days be x then,
27 : 36 :: 18 : x
[Please pay attention, we have written 27 : 36 rather than 36 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]
=>27x = 36 * 18
=> x = 24
So 24 days will be required to get work done by 27 men.
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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: D
Let x men can do the in 12 days and the required number of days be z
More men, Less days [Indirect Proportion]
Less work, Less days [Direct Proportion ]
men2x:xwork1:12 :: 12 : z
∴2x×1×z=x×12×12
⇒z=3
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