Model 1 Basics on Time & Work Practice Questions Answers Test with Solutions & More Shortcuts

Question : 1 [SSC CGL Prelim 2007]

A alone can complete a work in 12 days. A and B together can complete it in 8 days. How long will B alone take to complete the work ?

a) 20 days

b) 16 days

c) 24 days

d) 18 days

Answer: (c)

A’s 1 day’s work = $1/12$

(A+B)’s 1 day’s work = $1/8$

B’s 1 day’s work =$1/8 - 1/12 = {3 - 2}/24 = 1/24$

B alone can do the work in 24 days.

Using Rule 4,

Time taken by B = ${12 × 8}/{12 - 8}$ = 24 days

Question : 2 [SSC CGL Tier-I 2010]

If A and B together can complete a piece of work in 15 days and B alone in 20 days, in how many days can A alone complete the work ?

a) 30 days

b) 40 days

c) 60 days

d) 45 days

Answer: (c)

(A + B)’s 1 day’s work = $1/15$

B’s 1 day’s work = $1/20$

A’s 1 day’s work = $1/15 - 1/20 = {4 - 3}/60 = 1/60$

A alone will do the work in 60 days.

Using Rule 4,

A alone do in = ${15 × 20}/{20 - 15}$

= ${15 × 20}/5$ = 60 days

Question : 3 [SSC (South Zone) Investigator 2010]

If A and B together can complete a work in 12 days, B and C together in 15 days and C and A together in 20 days, then B alone can complete the work in

a) 20 days

b) 24 days

c) 30 days

d) 25 days

Answer: (a)

(A + B)’s 1 day’s work = $1/12$

(B + C)’s 1 day’s work = $1/15$

(C + A)’s 1 day’s work = $1/20$

On adding,

2 (A + B + C)’s 1 day's work = $1/12 + 1/15 + 1/20$

= ${5 + 4 + 3}/60 = 1/5$

(A+B+C)’s 1 day’s work = $1/10$

B’s 1 day’s work = $1/10 - 1/20 = {2 - 1}/20 = 1/20$

B alone can do the work in 20 days.

Using Rule 19,

B alone can do in = ${2 × 12 × 15 × 20}/{-12 × 15 + 15 × 20 + 20 × 12}$

= ${24 × 300}/{-180 + 300 + 240} = {24 × 300}/360$ = 20 days

Question : 4 [SSC CGL Prelim 2005]

A and B can do a piece of work in 12 days, B and C in 8 days and C and A in 6 days. How long would B take to do the same work alone ?

a) 48 days

b) 40 days

c) 24 days

d) 32 days

Answer: (a)

(A + B)'s 1 day's work = $1/12$ ...(i)

(B + C)'s 1 day's work = $1/8$ ...(ii)

(C + A)'s 1 day's work = $1/6$ ...(iii)

On adding,

2(A + B + C)'s 1 day's work = $1/12 + 1/8 + 1/6$

= ${2 + 3 + 4}/24 = 9/24$

(A+ B + C)'s 1 day’s work = $9/{24 × 2} = 9/48$ ...(iv)

On, subtracting (iii) from (iv),

B’s 1 day’s work = $9/48 - 1/6$

= ${9 - 8}/48 = 1/48$

B can complete the work in 48 days.

Using Rule 19,

B alone can do in = ${2 × 12 × 8 × 6}/{-12 × 8 + 8 × 6 + 6 × 12}$

= ${24 × 48}/{-96 + 48 + 72} = {24 × 48}/{-96 + 120}$

= ${24 × 48}/24$ = 48 days

Question : 5 [SSC CPO 2011]

A and B working together; can do a piece of work in 4$1/2$ hours. B and C working together can do it in 3 hours. C and A working together can do it in 2$1/4$ hours. All of them begin the work at the same time. Find how much time they will take to finish the piece of work.

a) 3·25 hours

b) 2·5 hours

c) 3 hours

d) 2 hours

Answer: (d)

(A + B)’s 1 hour’s work = $2/9$ .....(i)

(B + C)’s 1 hour’s work = $1/3$ ......(ii)

(C + A)’s 1 hour’s work = $4/9$ .....(iii)

Adding all three equations,

2 (A + B + C)’s 1 hour’s work = $2/9 + 1/3 + 4/9$

${2 + 3 + 4}/9$ = 1

A, B and C together will complete the work in 2 hours.

Using Rule 5,

Time taken = ${2 × 9/2 × 3 × 9/4}/{9/2 × 3 + 3 × 9/4 + 9/2 × 9/4}$

= ${{18 × 27}/8}/{27/2 + 27/4 + 81/8}$

= ${18 × 27}/8 × 8/({108 + 54 + 81})$

= ${18 × 27}/243$ = 2 hours

IMPORTANT quantitative aptitude EXERCISES

Model 1 Basics on Time & Work Shortcuts »

Click to Read...

Model 1 Basics on Time & Work Online Quiz

Click to Start..

Recently Added Subject & Categories For All Competitive Exams

Coded Inequalities Reasoning Questions & Answers For Bank

New 150+ Coded Inequalities Verbal Reasoning Multiple-Choice Questions and Answers Free Practice Test & Online Quiz PDF For All IBPS PO SO & CLERK 2024 Exams

28-Nov-2023 by Careericons

Continue Reading »

150+ Problem Solving Questions and Answers For Bank Exams

Problem-Solving Verbal Reasoning Concepts based Multiple Choice Questions and Answers Mock Test & Online MCQ Quiz for All 2024 Upcoming IBPS PO Clerk SO Exam

28-Nov-2023 by Careericons

Continue Reading »

New 150+ Syllogism Verbal MCQ Test PDF For IBPS RRB Exams

Free Syllogism Practice Multiple Choice Questions with Solved Answer PDF and All Verbal Reasoning Topics Online Mock Test For IBPS RRB PO & Clerk Exams 2024.

27-Nov-2023 by Careericons

Continue Reading »

New 200+ Syllogism Questions & Answers PDF For SSC Exams

Free Verbal Reasoning Syllogism Multiple Choice Questions with Solved Answer PDF & Online Mock Test. Prepare for all upcoming SSC CGL, CHSL, MTS Exams 2024

25-Nov-2023 by Careericons

Continue Reading »