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CHAIN RULE - MCQ Test (1) - UPSC MCQ


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16 Questions MCQ Test - CHAIN RULE - MCQ Test (1)

CHAIN RULE - MCQ Test (1) for UPSC 2024 is part of UPSC preparation. The CHAIN RULE - MCQ Test (1) questions and answers have been prepared according to the UPSC exam syllabus.The CHAIN RULE - MCQ Test (1) MCQs are made for UPSC 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for CHAIN RULE - MCQ Test (1) below.
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CHAIN RULE - MCQ Test (1) - Question 1
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If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the samerate?

Detailed Solution for CHAIN RULE - MCQ Test (1) - Question 1

Option C

Explanation :cost of x metres of wire = Rs. dcost of 1 metre of wire = Rs.(d/x)cost of y metre of wire = Rs.(y×d/x)=Rs. (yd/x)

CHAIN RULE - MCQ Test (1) - Question 2
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In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, howmany men will be catered to with remaining meal?

Detailed Solution for CHAIN RULE - MCQ Test (1) - Question 2

Option B

Explanation :Meal for 200 children = Meal for 120 menMeal for 1 child = Meal for 120/200 menMeal for 150 children = Meal for (120×150)/200 men=Meal for 90 menTotal mean available = Meal for 120 menRenaming meal = Meal for 120 men ‐ Meal for 90 men = Meal for 30 men

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CHAIN RULE - MCQ Test (1) - Question 3
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36 men can complete a piece of work in 18 days. In how many days will 27 men complete thesame work?

Detailed Solution for CHAIN RULE - MCQ Test (1) - Question 3

Option D

Explanation :Let the required number of days be xMore men, less days (indirect proportion)Hence we can write asMen36:27}::x:18 ⇒36×18=27×x ⇒12×18=9×x⇒12×2=x⇒x=24

CHAIN RULE - MCQ Test (1) - Question 4
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A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. If the smaller wheel has made21 revolutions, what will be the number of revolutions made by the larger wheel?
Detailed Solution for CHAIN RULE - MCQ Test (1) - Question 4

Option D

Explanation :Let the number of revolutions made by the larger wheel be xMore cogs, less revolutions (Indirect proportion)Hence we can write asCogs 6:14}: x: 21 ⇒6×21=14×x ⇒6×3=2×x ⇒3×3=x ⇒x=9

CHAIN RULE - MCQ Test (1) - Question 5
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3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day should 4pumps work in order to empty the tank in 1 day?
Detailed Solution for CHAIN RULE - MCQ Test (1) - Question 5

Option B

Explanation :Let the required hours needed be xMore pumps, less hours (Indirect proportion)More Days, less hours (Indirect proportion)Hence we can write asPumps 3:4::x:8Days 2:1⇒3×2×8=4×1×x⇒3×2×2=x⇒x=12

CHAIN RULE - MCQ Test (1) - Question 6
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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?
Detailed Solution for CHAIN RULE - MCQ Test (1) - Question 6

Option D

Explanation :Let the required number of days be xMore persons, less days (indirect proportion)More hours, less days (indirect proportion)Hence we can write asPersons 39:30::x:12Hours 5:6⇒39×5×12=30×6×x ⇒39×5×2=30×x ⇒39=3×x ⇒x=13

CHAIN RULE - MCQ Test (1) - Question 7
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A certain industrial loom weaves 0.128 meters of cloth every second. Approximately how manyseconds will it take for the loom to weave 25 meters of cloth?
Detailed Solution for CHAIN RULE - MCQ Test (1) - Question 7

Option D

Explanation :Let the required number of seconds be xMore cloth, More time, (direct proportion)Hence we can write asCloth 0.128:25} :: 1:x⇒0.128x=25 ⇒x=25/0.128 ⇒25000/128=3125/16≈195

CHAIN RULE - MCQ Test (1) - Question 8
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21 goats eat as much as 15 cows. How many goats each as much as 35 cows?
Detailed Solution for CHAIN RULE - MCQ Test (1) - Question 8

Option A

Explanation :15 cows ≡ 21 goats1 cow ≡21/15 goats35 cows ≡ (21×35)/15 goats≡(21×7)/3 goats≡7×7 goats ≡ 49 goats

CHAIN RULE - MCQ Test (1) - Question 9
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In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat onebag of husk?
Detailed Solution for CHAIN RULE - MCQ Test (1) - Question 9

Option B

Explanation :Assume that in x days, one cow will eat one bag of husk.More cows, less days (Indirect proportion)More bags, more days (direct proportion)Hence we can write asCows 40:1 ::x:40Bags 1:40⇒40×1×40=1×40×x ⇒x=40

CHAIN RULE - MCQ Test (1) - Question 10
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. If a quarter kg of potato costs 60 paise, how many paise does 200 gm cost?
Detailed Solution for CHAIN RULE - MCQ Test (1) - Question 10

Option D

Explanation :Let 200 gm potato costs x paiseCost of ¼ Kg potato = 60 Paise=> Cost of 250 gm potato = 60 Paise (∵ 1 Kg = 1000 gm => ¼ Kg = 1000/4 gm = 250 gm)More quantity, More Paise (direct proportion)Hence we can write asQuantity 200:250} :: x:60⇒200×60=250×x ⇒4×60=5×x ⇒4×12=x ⇒x=48

CHAIN RULE - MCQ Test (1) - Question 11
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A contract is to be completed in 56 days if 104 persons work, each working at 8 hours a day. After30 days, 2/5 of the work is completed. How many additional persons should be deployed so that thework will be completed in the scheduled time, each person’s now working 9 hours a day.
Detailed Solution for CHAIN RULE - MCQ Test (1) - Question 11

Option D

Explanation :Persons worked = 104Number of hours each person worked per day = 8Number of days they worked = 30Work completed = 2/5Remaining days = 56 ‐ 30 = 26Remaining Work to be completed = 1 ‐ 2/5 = 3/5Let the total number of persons who do the remaining work = xNumber of hours each person needs to be work per day = 9More days, less persons(indirect proportion) More hours, less persons(indirect proportion)More work, more persons(direct proportion)Hence we can write asDays 30:26Hours 8:9 ::x:104Work 35:25⇒30×8×3/5×104=26×9×2/5×x⇒x=(30×8×3/5×104)/(26×9×2/5)=(30×8×3×104)/(26×9×2)=(30×8×104)/(26×3×2)=(30×8×4)/(3×2)=5×8×4=160Number of additional persons required = 160 ‐ 104 = 56

CHAIN RULE - MCQ Test (1) - Question 12
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x men working x hours per day can do x units of a work in x days. How much work can becompleted by y men working y hours per day in y days?
Detailed Solution for CHAIN RULE - MCQ Test (1) - Question 12

Option B

Explanation :Let amount of work completed by y men working y hours per in y days = w unitsMore men, more work(direct proportion)More hours, more work(direct proportion)More days, more work(direct proportion)Hence we can write asMen x:yHours x:y ::x:wDays x:y⇒x3w=y3x ⇒w=y3x/x3=y3/x2

CHAIN RULE - MCQ Test (1) - Question 13
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A flagstaff 17.5 m high casts a shadow of length 40.25 m. What will be the height of a building,which casts a shadow of length 28.75 m under similar conditions?
Detailed Solution for CHAIN RULE - MCQ Test (1) - Question 13

Option A

Explanation :Let the required height of the building be x meterMore shadow length, More height (direct proportion)Hence we can write asShadow length 40.25:28.75}:: 17.5:x⇒40.25×x=28.75×17.5 ⇒x=(28.75×17.5)/40.25=(2875×175)/40250= (2875×7)/1610=2875/230=575/46=12.5

CHAIN RULE - MCQ Test (1) - Question 14
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If the price of 357 apples is Rs.1517.25, what will be the approximate price of 49 dozens of suchapples?
Detailed Solution for CHAIN RULE - MCQ Test (1) - Question 14

Option A

Explanation :Let the required price be xMore apples, More price (direct proportion)Hence we can write asApples 357:(49×12)} :: 1517.25:x⇒357x = (49×12)×1517.25 ⇒x = (49×12×1517.25)/357=(7×12×1517.25)/51= (7×4×1517.25)/17=7×4×89.25≈2500

CHAIN RULE - MCQ Test (1) - Question 15
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9 engines consume 24 metric tonnes of coal, when each is working 8 hours day. How much coal isrequired for 8 engines, each running 13 hours a day, if 3 engines of former type consume as much as4 engines of latter type?
Detailed Solution for CHAIN RULE - MCQ Test (1) - Question 15

Option D

Explanation :Let required amount of coal be x metric tonnesMore engines, more amount of coal (direct proportion)If 3 engines of first type consume 1 unit, then 1 engine will consume 1/3 unit which is its the rate ofconsumption.If 4 engines of second type consume 1 unit, then 1 engine will consume 1/4 unit which is its the rateof consumptionMore rate of consumption, more amount of coal (direct proportion)More hours, more amount of coal(direct proportion)Hence we can write asEngines 9:8rate of consumption 13:14 ::24:xhours 8:13⇒9×1/3×8×x=8×1/4×13×24 ⇒3×8×x=8×6×13 ⇒3xX=6×13 ⇒x=2×13=26

CHAIN RULE - MCQ Test (1) - Question 16
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In a camp, food was was sufficient for 2000 people for 54 days. After 15 days, more people cameand the food last only for 20 more days. How many people came?
Detailed Solution for CHAIN RULE - MCQ Test (1) - Question 16

Option A

Explanation :Given that food was sufficient for 2000 people for 54 daysHence, after 15 days, the remaining food was sufficient for 2000 people for 39 days (∵ 54 ‐ 15 =39)Let x number of people came after 15 days.Then, total number of people after 15 days = (2000 + x)Then, the remaining food was sufficient for (2000 + x) people for 20 daysMore men, Less days (Indirect Proportion) ⇒Men 2000:(2000+x)} :: 20:39⇒2000×39=(2000+x)20 ⇒100×39=(2000+x) ⇒3900=2000+x ⇒ x=3900−2000=1900

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