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

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