SSC CGL TIME AND WORK MCQ ENGLISH

Correct Answer : (B)

Explanation : Given:2 men and 3 women can do a work in 6 days3 men and 9 women can complete the work in 3 daysCalculation:Let the efficiency of man be M and woman be WAccording to question,(2M+3W)×6=(3M+9W)×3⇒12M+18W=9M+27W⇒12M−9M=27W−18W⇒3M=9W⇒1M=3W⇒1W=(13)M⇒12W={(13)×12}M⇒12W=4M∴ The amount of work done by 12 women is equal to the work of 4 men.

Correct Answer : (C)

Explanation : Let, A can complete the task in = x daysB can complete the task in = y daysAccording to the question,1x + 1y = 11.2⇒ x + y = xy1.2 …(i)A completes half the job in = x2 days and B completes half the job in = y2 days⇒ x2 + y2 = 2.5⇒ x + y = 5 …(ii)From (i) and (ii), we get,xy1.2 = 5⇒ xy = 6⇒ x = 6y …(iii)From (ii) and (iii) we get,6y + y = 5⇒ 6 + y2 = 5y⇒ y2 – 3y – 2y + 6 = 0⇒ y(y – 3) – 2(y – 3) = 0⇒ (y – 3) (y – 2) = 0⇒ y = 3 or 2For y = 3, x = 63 = 2For y = 2, x = 62 = 3∵ B is more efficient than A∴ B take less days than A∴ B would take 2 days to complete the task.

Correct Answer : (B)

Explanation : Formula:Per day Income = Total IncomeNumber of daysCalculation:Total income of A, B and C is = 20343 = Rs. 678 Per dayTotal income of A and C = 8502 = Rs. 425 Per dayPer day income of B = (678 – 425) Rs. = Rs. 253Total income of B and C together = 23505 = Rs. 470 Per day∴ Per day income of C = 470 – 253 = Rs. 217

Correct Answer : (D)

Explanation : Given:Total wages = Rs. 960Bhavesh share = Rs. 540Amar can complete the work = 6 daysBhavesh can complete the work = 12 daysCalculation:So, Amar share = Rs. 420Ratio of wages by Amar to Bhavesh = 420 : 540= 7 : 9Efficiency of ratio of Amar to Bhavesh = 16 : 112= 2 : 1Ratio of time of Amar to Bhavesh to complete the work together = WagesEfficiencyRatio of time of Amar to Bhavesh to complete the work together = 7921Ratio of time of Amar to Bhavesh to complete the work together = 718∴ Ratio of time of Amar to Bhavesh to complete the work together is = 7 : 18

Correct Answer : (D)

Explanation : Time taken by Mukesh =14 daysTime taken by Shivam =16 daysTime taken by Mukesh, Shivam and Harsh =6 daysTotal work = LCM of 14,16 and 6=336 units⇒ Efficiency of Mukesh =33614=24 units/day⇒ Efficiency of Shivam =33616=21 units/day⇒ Efficiency of Mukesh, Shivam and Harsh together =3366=56units/day⇒ Efficiency of Harsh = Total efficiency – Efficiency of (Mukesh +Shivam)⇒ Efficiency of Harsh =56−(24+21)=56−45=11 units/dayFor 56 units they get = Rs. 2800⇒1 unit = Rs. 50∴ Harsh’s salary =11×50= Rs. 550

Correct Answer : (B)

Explanation : Given,P’s 1 day work =130Q’s 1 day work =120As we know,Work = Efficiency × TimeP’s 18 day work =1830=35Remaining work =1−35=25Q’s 25 day work =120×52=18Q will complete the remaining job alone in 8 days.

Correct Answer : (C)

Explanation : If A can do a piece of work in x days and B can do it in y days then A and B working together will do the same work in work in (xyx+y) days.A’s time =x=20 daysB’s time =y=15 daysA+B can do the work =20×1520+15 days=30035=607=847 days

Correct Answer : (A)

Explanation : Given:12 men can complete a work in 10 days. 25 women can complete the same work in 6 days.Calculation:Let the work efficiency of a man and a woman be M and W respectively.We know that,Total work = Efficiency × DaysAccording to the question,Total work = 12 M × 10 = 25 W × 6⇒ MW = 54Total work = 12 × 5 × 10 = 600 unitSo, 8 men and 4 women can complete the same work, working together.600(8 × 5 + 4 × 4) = 60056⇒ 757 = 1057 days

Correct Answer : (C)

Explanation : Given:A can do 25 of a work in 10 days.B can do 12 of the some work in 10 days.Calculation:Let, the total work be 100 units.So, (25)×100=40 unitsA can do 40 units in 10 days.Also, (12)×100=50 unitsB can do 50 units in 10 days.Efficiency of A=4010=4 units/dayEfficiency of B=5010=5 units/dayEfficiency of (A+B)=9 units/dayThey both work together for 5 days.Work done in 5 days =9 units / day ×5 days =45 unitsRemaining work = Total work – Work done =100−45=55 unitsTime taken to complete the work alone =555=11 days

Correct Answer : (A)

Explanation : Given,1 day work of T =112Let U alone can complete the work in x days.1 day work of U =1xTime taken by T and U to complete one-third work = 3 daysTime taken by T and U in completing 1 full piece of work =3÷(13) days = 9 days1 day work of T and U working together =19⇒(112)+(1x)=19⇒1x=(19)−(112)⇒x=36 days

Correct Answer : (D)

Explanation : Given:A can complete a piece of task in =10hrs .B and C together can complete in =12hrs .A and C together can complete it in =6hrs .Formula:Total work = Efficiency × Time TakenCalculation:Total work =60 unit ( LCM of 10,12,6)Efficiency of A=6010=6 units / dayEfficiency of C=(606)−6=4 units / dayEfficiency of B=(6012)−4=1 units/day∴ B alone can complete the whole work in =601=60 hrs.

Correct Answer : (D)

Explanation : Given:Total number of hired people = 2525 people can complete the work in 60 days.The company hires 10 more persons after every 5 days.Formula:Total work = total employees × total timeCalculation:Total number of hired people = 2525 people can complete the work in 60 days.Total work = 25 × 60 = 1500 unitsSo work done by 25 people in first 5 days = 25 × 5 = 125 unitsThe company hires 10 more persons after every 5 days.Now total number of people = 25 + 10 = 35So work done by 35 people in next 5 days = 35 × 5 = 175 unitsAgain in next five days, total number of people = 35 + 10 = 45So work done by 45 people in next 5 days = 45 × 5 = 225 unitsAgain in next five days, total number of people = 45 + 10 = 55So work done by 55 people in next 5 days = 55 × 5 = 275 unitsAgain in next five days, total number of people = 55 + 10 = 65So work done by 65 people in next 5 days = 65 × 5 = 325 unitsAgain in next five days, total number of people = 65 + 10 = 75So work done by 75 people in next 5 days = 75 × 5 = 375 unitsTotal work that done = 125 + 175 + 225 + 275 + 325 + 375 = 1500 unitsThus the total work is done.Now time taken by people to complete work = 5 + 5 + 5 + 5 + 5 + 5 = 30 daysNumber of days before the work will be finished = 60 – 30 = 30 days∴ The work will be finished before 30 days.

Correct Answer : (B)

Explanation : Given:Time taken by A to finish a task alone =24 daysCalculation:Let the total work be =1A alone can finish the task in 24 days⇒A′ s one-day work =1/24A and B complete the whole task in =1113 daysA and B work on alternate days, with B beginning so, we can say B will work only 6 days⇒ A will work only 1113−6=513 daysIf A′ s one day work =1/24 of work A completes in 1 day⇒ A’s 513 days work =1/24×513=1/24×16/3⇒2/9Remaining work =1−2/9=7/9∴ B does the 7/9th part of the work in 6 days.

Correct Answer : (A)

Explanation : Since B is 50% more efficient than A.Ratio of efficiency of A to B = 100 ∶ 150 = 2 ∶ 3The ratio of time taken by A to B to finish the work = 12 ∶ 13 = 3 ∶ 2Let the time taken by A and B alone to do work be 3x and 2x respectively.According to the question,3x – 2x = 6⇒ x = 6Time taken by A and B alone to do work is 18 days and 12 days respectively.The efficiency of A and B when they work together = 118 + 112 = 536The required time is taken when both A and B together started working = 365 = 7.2 days

Correct Answer : (C)

Explanation : Given:Time taken by Samrat and Kamlesh to do the work together = 18 daysCalculation:Let the time taken by Samrat and Kamlesh to do the work alone be x and y respectively.Then, Samrat’s and Kamlesh’s 1 day work = 1x and 1y respectivelyTotal work = 1x + 1y = 118 —-(i)Samrat worked thrice as efficiently and then Kamlesh worked with half his efficiency it will take same time to finish the work.Samrat’s 1 day work = 3xKamlesh’s 1 day work = 12yTime taken by them to finish the work = 18 daysTotal work = 3x + 12y = 118 —-(ii)Multiplying (i) by 3 and subtracting (ii) by (i),3x+3y-3x-12y=318-118⇒ 3y-12y=19⇒ y = 452Putting the value of y in (ii), we get⇒ 3x+1×22×45=118⇒ 3x=118-145⇒ 3x=5-245⇒ 3x=390⇒ x = 90∴ Time taken by Samrat to finish the work alone is 90 days.

Correct Answer : (A)

Explanation : Let the time taken by A, B, C and D alone to do that work is A, B, C and D days respectively.According to the question,1A + 1B + 1C = 14.8 —-(1)1A + 1C = 16 —- (2)From (1) and (2),16 + 1B = 14.8⇒ 1B=14.8-16⇒ 1B=5-424B = 24 daysGiven that:1B + 1D = 116⇒ 124 + 1D = 116⇒ 1D=116-124⇒ 1D=3-248D = 48 days

Correct Answer : (D)

Explanation : Given:Total amount = Rs. 13200Work done by (A + B) = 511 workWork done by (C + D) = 12 workConcept used:Work done ∝ WagesCalculation:Work done by (A + B + C + D + E) = 1 unitWork done by (A + B) + (C + D) = 511 + 12Net work done by (A + B) + (C + D) = 2122Work done by E = 1 – 2122 = 122Ratio of work of (A + B) : (C + D) : E = 511 : 12 : 122= 10 : 11 : 1Ratio of wages of (A + B) : (C + D) : E = 10 : 11 : 1Share of E = 13200 × 122= 600∴ The amount received by E for the work is Rs. 600

Correct Answer : (A)

Explanation : Tap A can fill the tank =180 minutesTap A ’s one-minute work =1180Tap B can fill the tank =20 minutesTap B ’s one-minute work =120Tap C can fill the tank =90 minutesTap C ’s one-minute work =190When all the taps are opened together,A+B+C=(1180+120+190)=(1+9+2)180=12180=115So, (A+B+C) working together can fill the whole tank in 15 minutes.

Correct Answer : (A)

Explanation : Let total work be 60x units (LCM of 10,15,60 )Efficiency of A=6x units/dayEfficiency of B=4x units/dayEfficiency of C=x units/dayWork done in 5 days by A and B=(6x+4x)×5=50x unitsRemaining work =60x−50x=10x unitsThis work is completed by B and C .Time taken to complete the remaining work =10x(4x+x)=10x5x=2 days∴ Total time taken to complete the work =5+2=7 days

Correct Answer : (C)

Explanation : Given:Length of the side of square-shaped field = 10 mTime taken by A to plough the field = 10 hoursTime taken by B to plough the field = 5 hoursPercentage increase in the side of the new square-shaped field = 50%Formula:Area of Square = (side)2Work efficiency = (Total Work)(Total time)Calculation:Area of the field to be ploughed = (side)2 = 100 m2The efficiency of A to plough the field = (Area of field)(Total Time)= 10010 = 10 m2/hour —(1)The efficiency of B to plough the field = (Area of field)(Total Time)= 1005 = 20 m2/hour —(2)Length of side of new field = 10 + 10×50100= 10 + 5 = 15 mArea of new field = (side)2= 152= 225 m2Colletive efficiency of A and B = (10 + 20) m2/hour —(By adding (1) and (2))= 30 m2/hourTotal time taken by A and B to plough together = (Area of field)(Collective efficiency of A and B)= 22530= 7.5 hours∴ A and B will take 7.5 hours to plough the new field.

Correct Answer : (B)

Explanation : Let X be the initial number of men then,According to the question,4X=X+(X−20)+(X−40)+(X−60)+(X−80)+(X−100)+(X−120)⇒4X=7X−420⇒3X=420⇒X=4203⇒X=140 men

Correct Answer : (C)

Explanation : Formula:Total Work Done = Capacity × TimeCalculation:We are assuming total work is 1 unit.Let Capacity of A and B is x unit per day.And Capacity of C and D is y unit per day.According to the question,x = 2y ….(i)And, 1y – 1x = 12⇒ (x – y)xy = 12Now, putting x = 2y in above equation,(2y – y)2y2 = 12⇒ y = 24y2⇒ y = 124From equation (i) we get,⇒ x = 112So, Total time required = 1112 + 124= 24(2 + 1)= 8 days

Correct Answer : (D)

Explanation : Given:Time is taken by a man to do the work = 20 daysTime is taken by a woman to do the work = 30 daysTime is taken by a boy to do the work = 40 daysFormula:Total work = Efficiency × Time is takenCalculation:Let the total work be x unitsThe efficiency of a man = x20The efficiency of a woman = x30The efficiency of a boy = x40So the efficiency of 4 men = 4 × x20 = x5Now efficiency of 5 boys = 5 × x40 = x8The total efficiency of 4 men and 5 boys = x5 + x8 = 13×40Now the work is done by 4 men and 5 boys in 4 days.⇒ 4 × 13×40 units= 13×10 unitsRemaining work = 2x – initial work= 2x – 13×10 = 7×10So the remaining work is done in 1 day by women.Now the number of women = remaining workefficiency of a woman⇒ 7x10x30 = 21 women∴ Need 21 women assist to complete work in 1 day.

Correct Answer : (A)

Explanation : We know, Time × rate = workLet’s consider the work of building one wall to be 48 units. (LCM of 12, 16, and 24 )A total of 6 walls are to be built. i.e. 6 × 48 = 288 unitsABCTime121624Rate432Work484848Thus, rates of A, B, and C are 4, 3, and 2 respectively per day.Work done by A ( 1st 16 days) = 4 × 16 = 64Work done by B (next 12 days) = 3 × 12 = 36Total work done by A and B = 64 + 36 = 100 unitsWork remaining = 288 – 100 = 188 unitsSo, Work done by C = 188 = 2 × no. of days C has to work∴ No. of days C has to work =1882=94 days

Correct Answer : (A)

Explanation : Given:Ratio of efficiency of a man, woman and child =7:3:2Ratio of the number of days for which they work =3:9:11Total earning by working together = Rs. 7000Calculation:Share of the total work done by men, women and children =(7×3):(3×9):(2×11)⇒ Share of the total work done by men, women and children =21:27:22Total work done =(21+27+22)=70 unitsWage will be distributed in the ratio of work done by them70 units = Rs. 70001 unit =700070⇒1 unit = Rs. 100Share of work done by children =22 units⇒22 units =22×100⇒22 units = Rs. 2200∴ The income earned by children is Rs. 2200.

Correct Answer : (D)

Explanation : Given:2M + 5W + 6C = 72 hours4M + 10C = 90 hours3M + 5W = 120 hoursFormula:Efficiency = total work/total daysCalculation:Let total work be xTotal efficiency of 2M + 5W + 6C = x72 —-(1)Total efficiency of 4M + 10C = x90 —-(2)Total efficiency of 3M + 5W = x120 —-(3)Add equation (2) and (3),4M + 10C + 3M + 5W = x90 + x120⇒ 7M + 5W + 10C = (4x + 3x)360⇒ 7M + 5W + 10C = 7×360Total efficiency of 7M + 5W + 10C = 7×360 —-(4)Subtract equation (1) from equation (4),7M + 5W + 10C – (2M + 5W + 6C) = 7×360 – x72⇒ 5M + 4C = (7x – 5x)360⇒ 5M + 4C = 2×360Total efficiency of 5M + 4C = 2×360Time taken by 5M + 4C to complete the work = x2x360⇒ 3602 = 180 hours∴ Time taken by 5M + 4C to complete the work is 180 hours.

Correct Answer : (A)

Explanation : The efficiencies of A,B and C are in the ratio of 5:3:2 .Total work =(5+3+2)×21=21040% of the total work =210×40100=8440% of the total work completed by B in =843=28 hours

Correct Answer : (B)

Explanation : Ratio of times taken by Sakshi and Tanya =125:100=5:4Suppose Tanya takes x days to do the work.5:4:20:x⇒x=(4×205)⇒x=16 daysHence, Tanya takes 16 days to complete the work.

Correct Answer : (C)

Explanation : Given:A can finish the work = 6 daysB can finish the work = 12 daysC can finish the work = 15 daysTime taken by D to finish the remaining work = 2 daysFormula:Total Work Done = Capacity × TimeCalculation:We are assuming total work is 1 unit.1 day work of A = 161 day work of B = 1121 day work of C = 115Total work of A, B, and C in 3 days = 16+112+115×3Remaining work after 3 days = 1 – 16 + 112 + 115 × 3= 1 – 12 + 14 + 15= 1 – (10 + 5 + 4)20= 1 – 1920= 120 unitD completed the 120 unit of work = 2 daysSo, he will do 1 unit of work = 20×2 = 40 days∴ Time taken by D to finish the whole work = 40 days.

Correct Answer : (B)

Explanation : Given:Days taken by A to complete the work =18 daysB is 12.5% more efficient than AConcept used:Efficiency is inversely proportional to the time.Calculation:12.5%=18Let efficiency of A be 8 unitsAnd efficiency of B be 9 units.A : B (Efficiency) = 8 : 9A : B (Time)= 9 :8From this,Time taken by A=9 units⇒9 units =18 days⇒1 unit =2 days⇒8 units =2×8=16 daysTake L.C.M. of 16,18 and make it as total work i.e. 144 units Total work =144 unitsTotal efficiency A+B=8+9=17 unitsTime taken =14417=8817∴ The time taken by A and B to complete the work together is 8817 days.