Question 1

In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days will one cow eat one bag?

Accepted Answer

Given data 40 cows consume 40 bags in 40 days. Concept / Approach Use the work-rate idea: consumption is proportional to (number of cows) × (days). Step-by-step calculation Let r = bags consumed per cow per day.Total bags = (cows) × (days) × r ⇒ 40 = 40 × 40 × rr = 40 / 1600 = 1/40 bag per cow per dayTime for 1 cow to consume 1 bag = 1 ÷ (1/40) = 40 days Final Answer 40 days

Question 2

36 men can finish a job in 18 days. In how many days will 27 men complete the same work (same efficiency)?

Accepted Answer

Concept / Approach Assuming equal efficiency, Work = Men × Days (constant for the same job). Step-by-step calculation 36 × 18 = 27 × DD = (36 × 18) ÷ 27 = (4/3) × 18 = 24 Quick check Fewer men (27 < 36) ⇒ more days; 24 > 18, consistent. Final Answer 24 days

Question 3

Three pumps, each working 8 hours per day, can empty a tank in 2 days. How many hours per day must four pumps work to empty the tank in 1 day?

Accepted Answer

Given data 3 pumps × 8 h/day × 2 days empty the tank Find hours/day for 4 pumps to finish in 1 day Concept / Approach Total work (emptying the tank) is proportional to the total pump-hours. So, (number of pumps) × (hours per day) × (days) = constant for the same tank. Step-by-step calculation Total pump-hours needed = 3 × 8 × 2 = 48 pump-hoursLet required hours/day for 4 pumps be H. Then 4 × H × 1 = 48H = 48 ÷ 4 = 12 hours/day Verification 4 pumps × 12 h = 48 pump-hours, same as original requirement. Common pitfalls Adding or averaging times; this is a direct work (rate × time) problem. Final Answer 12 hours/day

Question 4

Four mat-weavers weave 4 mats in 4 days. At the same rate, how many mats will 8 mat-weavers weave in 8 days?

Accepted Answer

Given data 4 weavers → 4 mats in 4 days Find mats made by 8 weavers in 8 days at the same rate Concept / Approach Mats are proportional to (number of weavers) × (days), assuming identical constant rates. Step-by-step calculation Baseline output per (weaver·day): k = 4 mats ÷ (4 weavers × 4 days) = 4/16 = 0.25For 8 weavers in 8 days: mats = 0.25 × 8 × 8 = 16 Alternative check Scaling factor = (8×8)/(4×4) = 64/16 = 4 ⇒ 4 mats × 4 = 16 mats. Common pitfalls Adding weavers and days instead of multiplying. Final Answer 16 mats

Question 5

A flagstaff 17.5 m high casts a 40.25 m shadow. Under similar conditions, what is the height of a building that casts a 28.75 m shadow?

Accepted Answer

Given data Flagstaff: height = 17.5 m, shadow = 40.25 m Building: shadow = 28.75 m; find its height Concept / Approach With the same sun elevation, triangles are similar ⇒ height is proportional to shadow length. Step-by-step calculation Height / Shadow = constantBuilding height = 17.5 × (28.75 / 40.25)= 17.5 × 0.713422… = 12.5 m Verification 17.5/40.25 ≈ 0.4348, 12.5/28.75 ≈ 0.4348 (matches). Common pitfalls Using inverse ratio (40.25/28.75) erroneously. Final Answer 12.5 m

Question 6

An industrial loom weaves 0.128 m of cloth per second. Approximately how many seconds are needed to weave 25 m of cloth?

Accepted Answer

Given data Speed = 0.128 m/s Distance (cloth length) = 25 m Concept / Approach Time = Distance / Speed, keeping units consistent (metres, seconds). Step-by-step calculation t = 25 / 0.128 = 195.3125 sApproximately = 195 s (nearest second) Verification 0.128 × 195 ≈ 24.96 m (very close to 25 m); rounding is appropriate for 'approximately'. Common pitfalls Inverting the fraction (using 0.128/25). Converting to minutes inadvertently (units must remain seconds). Final Answer 195 s

Question 7

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

Accepted Answer

Given data 7 spiders → 7 webs in 7 days. Concept / Approach Work is proportional to spider-days. Compute rate per spider-day. Step-by-step calculation Total spider-days = 7 spiders × 7 days = 49 spider-daysWebs made = 7 ⇒ rate = 7 / 49 = 1/7 web per spider-dayFor 1 spider to make 1 web: days = 1 ÷ (1/7) = 7 days Verification 1 spider in 7 days produces 1 web at 1/7 per day; scales consistently. Common pitfalls Assuming 1 day by symmetry; must consider rate via spider-days. Final Answer 7 days

Question 8

A camp has food for 120 men or 200 children. If 150 children have eaten, how many men can be fed with the remaining food?

Accepted Answer

Given data Food equivalent: 120 men ≡ 200 children 150 children have consumed their share Concept / Approach Use equivalence: 1 child = (120/200) man = 3/5 man. Convert remaining children-equivalents to men. Step-by-step calculation Remaining children-equivalents = 200 − 150 = 50 childrenConvert to men: 50 × (3/5) = 30 men Verification Alternatively, per child consumption = 1/200 of stock; leftover = 50/200 = 1/4 stock; 1/4 of 120 men = 30. Common pitfalls Using inverse factor 5/3 instead of 3/5 when converting children to men. Final Answer 30 men

Question 9

A wheel with 6 cogs meshes with a larger wheel with 14 cogs. When the smaller wheel makes 21 revolutions, how many revolutions does the larger wheel make?

Accepted Answer

Given data Small wheel: 6 cogs Large wheel: 14 cogs Small wheel revolutions = 21 Concept / Approach Teeth engagements are equal at the mesh. Total teeth passed by small wheel = total teeth passed on large wheel's rim. Revolutions are inversely proportional to the number of cogs. Step-by-step calculation Teeth passed by small wheel = 21 × 6 = 126 teethRevolutions of large wheel = 126 ÷ 14 = 9 Verification Inverse ratio check: revL / revS = 6/14 ⇒ revL = 21 × 6/14 = 9. Common pitfalls Using direct ratio 14/6 instead of inverse. Final Answer 9

Question 10

If the cost of x metres of wire is d rupees, what is the cost of y metres at the same rate?

Accepted Answer

Given data Cost for x m = d rupees Find cost for y m at same unit rate Concept / Approach Unit rate = (cost per metre) = d/x rupees per metre. Step-by-step calculation Cost for y m = (d/x) × y = (dy)/x rupees Verification For y = x, formula gives d rupees, consistent. Common pitfalls Using dx/y (that would be cost for x/y metres). Final Answer dy/x rupees

Question 11

Six identical machines produce 270 bottles per minute at a constant rate. At this rate, how many bottles can ten such machines produce in four minutes?

Accepted Answer

Given data 6 machines → 270 bottles/min Find output of 10 machines in 4 minutes Concept / Approach Rate per machine is constant; total rate scales linearly with number of machines. Step-by-step calculation Per-machine rate = 270 / 6 = 45 bottles/min10 machines rate = 10 × 45 = 450 bottles/minIn 4 minutes: 450 × 4 = 1800 bottles Verification Proportionality check: factor (10/6) in machines and ×4 minutes ⇒ 270 × (10/6) × 4 = 270 × (5/3) × 4 = 270 × (20/3) = 90 × 20 = 1800. Common pitfalls Multiplying by 6 again or forgetting the 4-minute duration. Final Answer 1800 bottles

Question 12

If a quarter kilogram of potatoes costs 60 paise, how many paise will 200 grams cost?

Accepted Answer

Given data 0.25 kg costs 60 paise Find cost for 200 g (= 0.2 kg) Concept / Approach Use unitary method (cost is proportional to weight). Step-by-step calculation Cost per kg = 60 ÷ 0.25 = 240 paise/kgCost for 0.2 kg = 240 × 0.2 = 48 paise Verification Proportion check: 200 g is 4/5 of 250 g; 4/5 × 60 = 48 paise. Common pitfalls Converting grams to kg incorrectly or mixing paise and rupees. Final Answer 48 paise

Question 13

A fort has food for 150 men for 45 days. After 10 days, 25 men leave. For how many days will the remaining food last?

Accepted Answer

Given data Initial capacity: food for 150 men for 45 days After 10 days at 150 men, 25 men leave ⇒ remaining men = 125 Concept / Approach Use man-days: total food = (men) × (days). Food consumed is proportional to men × time. Step-by-step calculation Total food (man-days) = 150 × 45 = 6750Food used in first 10 days = 150 × 10 = 1500Remaining food (man-days) = 6750 − 1500 = 5250With 125 men, days left = 5250 ÷ 125 = 42 Verification 42 × 125 = 5250 man-days, matching the remainder. Common pitfalls Subtracting days instead of using man-days. Forgetting that the consumption rate changes when men leave. Final Answer 42 days

Question 14

A man completes 5⁄8 of a job in 10 days. At this rate, how many more days are needed to finish the job?

Accepted Answer

Given data Work done in 10 days = 5/8 of job Concept / Approach Rate = (work)/(time). Remaining work = 1 − 5/8 = 3/8. Step-by-step calculation Daily rate = (5/8) ÷ 10 = 1/16 of the job per dayTime for remaining 3/8 = (3/8) ÷ (1/16) = (3/8) × 16 = 6 Quick check Total time = 10 + 6 = 16 days → 16 × (1/16) = 1 job. Final Answer 6 days

Question 15

39 persons can repair a road in 12 days, working 5 hours per day. In how many days will 30 persons, working 6 hours per day, complete the work?

Accepted Answer

Concept / Approach Work is proportional to (persons) × (hours per day) × (days) when efficiency is constant. Step-by-step calculation Total work (person-hours) = 39 × 5 × 12 = 2340Daily capacity with 30 persons at 6 h/day = 30 × 6 = 180 person-hours/dayDays required = 2340 ÷ 180 = 13 Verification 13 × 180 = 2340 person-hours, equal to the original work. Final Answer 13 days

Question 16

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?

Accepted Answer

Let the required length be x meters More men, More length built (Direct proportion) Less days, Less length built (Direct Proportion) M e n 20 : 35 D a y s 6 : 3 ⋮ ⋮ 56 : x => (20 x 6 x X)=(35 x 3 x 56) => x = 49 Hence, the required length is 49 m.

Question 17

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?

Accepted Answer

Originally let there be x men. Less men, More days (Indirect Proportion) Therefore, (x-10) : x :: 100 :110 => (x - 10) * 110 = x * 100 => x= 110

Question 18

If 36 men can do a piece of work in 25 hours, in how mwny hours will15 men do it?

Accepted Answer

Let the required no of hours be x. Then Less men , More hours (Indirct Proportion) Therefore, 15:36 ::25:x => (15 x X)=(36 x 25) => x = 60 Hence, 15 men can do it in 60 hours.

Question 19

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

Accepted Answer

(2 x 14) men +(7 x 14) boys = (3 x 11) men + (8 x 11) boys =>5 men= 10 boys => 1man= 2 boys 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) B o y s 22 : 11 W o r k 1 : 3 ⋮ ⋮ 14 : x Therefore, (22 * 1 * x) = (11 * 3 * 14) => x = 21 Hence, the required number of days = 21

Question 20

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

Accepted Answer

Let the required number days be x. Less spiders, More days (Indirect Proportion) Less webs, Less days (Direct Proportion) S p i d e r s 1 : 7 W e b s 7 : 1 ⋮ ⋮ 7 : x => 1 * 7 * x = 7 * 1 * 7 => x= 7

Chain Rule Questions