# Model 1 Basics On Time & Work Section-Wise Topic Notes With Detailed Explanation And Example Questions

#### Top 10,000+ Aptitude Memory Based Exercises

The following question based on Time & Work topic of Quantitative Aptitude

Questions : 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

The correct answers to the above question in:

(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)

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

#### Discuss Form

Valid first name is required.
Your genuine comment will be useful for all users! Each and every comment will be uploaded to the question after approval.

#### Read more basics on time and work Based Quantitative Aptitude Questions and Answers

Question : 1

A and B can do a piece of work in 10 days, B and C in 15 days and C and A in 20 days. C alone can do the work in :

a) 30 days

b) 80 days

c) 60 days

d) 120 days

According to the question

Work done by A and B together in one day = \$1/10\$ part

Work done by B and C together in one day = \$1/15\$ part

Work done by C and A together in one day = \$1/20\$ part

So, A + B = \$1/10\$ ....(I)

B + C = \$1/15\$ ...(II)

C + A = \$1/20\$ ....(III)

Adding I, II, III, we get

2 (A + B + C) = \$1/10 + 1/15 + 1/20\$

2 (A + B + C) = \${6 + 4 + 3}/60 = 13/60\$

A + B + C = \$13/120\$ ....(IV)

Putting the value of eqn. (I) in eqn. (IV)

\$1/10 + C =13/120\$

C = \$13/120 - 1/10 = {13 - 12}/120 = 1/120\$

Work done in 1 day by C is \$1/120\$ part

Hence, C will finish the whole work in 120 days

Using Rule 19
A and B can do a work in 'x' days, B and C can do the same work in 'y' days. C and A can do the same work in 'z' days. Then, all can do alone the work as following:
A alone can do in =\${2xyz}/{xy + yz - zx}\$days
B alone can do in =\${2xyz}/{-xy + yz + zx}\$days
C alone can do in =\${2xyz}/{xy - yz + zx}\$days

Time Taken by C= \${2xyz}/{xy - yz + zx}\$

= \${2 × 10 × 15 × 20}/{10 × 15 - 15 × 20 + 20 × 10 }\$

= \$6000/{150 - 300 + 200} = 6000/50\$ = 120 days

Question : 2

A and B together can complete a piece of work in 18 days, B and C in 24 days and A and C in 36 days. In how many days, will all of them together complete the work ?

a) 10 days

b) 12 days

c) 16 days

d) 15 days

(A + B)’s 1 day’s work = \$1/18\$

(B + C)’s 1 day’s work = \$1/24\$

(A + C)’s 1 day’s work = \$1/36\$

2 (A + B + C)’s 1 day’s work= \$1/18 + 1/24 + 1/36\$

= \${4 + 3 + 2}/72 = 1/8\$

(A + B + C)’ 1 day’s work = \$1/16\$

A, B and C together will complete the work in 16 days.

Using Rule 5,

Total time taken = \${2 × 18 × 24 × 36}/{18 × 24 +24 × 36 + 36 × 18}\$

= \${36 × 24 × 36}/{432 + 864 + 648}\$

= \$31104/1944\$ = 16 days

Question : 3

A and B together can do a work in 8 days, B and C together in 6 days while C and A together in 10 days, if they all work together, the work will be completed in :

a) 4\$4/9\$ days

b) 5\$5/47\$ days

c) 3\$3/4\$ days

d) 3\$3/7\$ days

(A + B)'s 1 day's work = \$1/8\$ ...(i)

(B + C)'s 1 day's work = \$1/6\$ ...(ii)

(C + A)'s 1 day's work = \$1/10\$ ...(iii)

2(A + B + C)'s 1 day's work = \$1/8 + 1/6 + 1/10\$

= \${15 + 20 + 12}/120 = 47/120\$

(A + B + C)'s 1 day’s work= \$47/240\$

(A + B + C) together will complete the work in

\$240/47 = 5{5}/47\$ days.

Using Rule 5,

Time taken = \${2 × 8 × 6 × 10}/{8 × 6 + 6 × 10 + 10 × 8}\$

= \$960/{48 + 60 + 80} = 960/188\$

= \$240/47 = 5{5}/47\$ days

Question : 4

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

(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)

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

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

(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\$

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 : 6

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

(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

## Recently Added Subject & Categories For All Competitive Exams

#### Top 100+ English Jumbled Sentences MCQ with PDF for RBI

Very important Jumbled Sentences questions with answers PDF for RBI. 100+ General English practice exercises for all Bank, Govt, and Competitive Exams

19-Jul-2024 by Careericons

#### Top 199+ Percentage Aptitude Online Test For UPSC TNPSC

Problems on percentage aptitude problems solving with the help of allegations & mixture method. Get all easy, quick shortcuts, formulas, methods & techniques

18-Jul-2024 by Careericons

#### 100+ Quadratic Equations MCQ with Solution PDF for SBI

Top Quadratic Equations Aptitude MCQ questions with detailed solutions, download PDF. Practice 100+ model exercises for RBI, all Govt, and Competitive Exams

18-Jul-2024 by Careericons

#### Simple Interest Aptitude MCQ Questions Solutions PDF SBI

Recent Simple Interest Aptitude MCQ questions with detailed solutions, download PDF. Practice 100+ model exercises for RBI, all Govt, and Competitive Exams

18-Jul-2024 by Careericons