Model 1 Basics On Time & Work Practice Questions Answers Test With Solutions & More Shortcuts

Question : 11 [SSC CGL Tier-1 2011]

A and B together can do a work in 10 days. B and C together can do the same work in 6 days. A and C together can do the work in 12 days. Then A, B and C together can do the work in

a) 8$2/7$ days

b) 5$5/7$ days

c) 28 days

d) 14 days

Answer: (b)

(A + B)’s 1 day’s work = $1/10$

(B + C)’s 1 day’s work = $1/6$

(C + A)’s 1 day’s work = $1/12$

Adding all three

2 (A + B + C)’s 1 day’s work = $1/10 + 1/6 + 1/12$

${6 + 10 + 5}/60 = 21/60 = 7/20$

(A + B + C)’s 1 day’s work = $7/40$

All three together will complete the work in $40/7 = 5{5}/7$ = days

Using Rule 5,

Time taken = ${2 × 10 × 6 × 12}/{10 × 6 + 6 × 12 + 12 × 10}$

= $1440/{60 + 72 + 120}$

= $1440/252 = 40/7 = 5{5}/7$ days

Question : 12 [SSC CHSL 2010]

A, B and C together can complete a piece of work in 30 minutes. A and B together can complete the same work in 50 minutes. C alone can complete the work in

a) 150 minutes

b) 80 minutes

c) 60 minutes

d) 75 minutes

Answer: (d)

Work done by (A + B + C) in 1 minute = $1/30$

Work done by (A + B) in 1 minute = $1/50$

Work done by C alone in 1 minute = $1/30 - 1/50$

= ${5 - 3}/150 = 2/150 = 1/75$

C alone will complete the work in 75 minutes.

Using Rule 4,

C alone can do in = ${xy}/{x - y}$

= ${50 × 30}/{50 - 30}$ = 75 minutes

Question : 13 [SSC CGL Prelim 2005]

A can do a piece of work in 4 hours; B and C can do it in 3 hours. A and C can do it in 2 hours. How long will B alone take to do it ?

a) 24 hours

b) 8 hours

c) 10 hours

d) 12 hours

Answer: (b)

A’s 1 hour’s work = $1/4$

(B + C)’s 1 hour’s work = $1/3$

(A + C)’s 1 hour’s work = $1/2$

C’s 1 hour’s work

= $1/2 - 1/4 = {2 - 1}/4 = 1/4$

and B’s 1 hour’s work

= $1/3 - 1/4 = {4 - 3}/12 = 1/12$

Hence, B alone can do the work in 12 hours.

Question : 14 [SSC CGL Prelim 2008]

While working 7 hours a day, A alone can complete a piece of work in 6 days and B alone in 8 days. In what time would they complete it together, working 8 hours a day ?

a) 3.6 days

b) 2.5 days

c) 3 days

d) 4 days

Answer: (c)

A alone can complete the work in 42 days working 1 hour daily. Similarly, B will take 56 days working 1 hour daily.

A 's 1 day's work = $1/42$

B 's 1 day's work = $1/56$

(A + B) 's 1 day's work = $1/42 + 1/56 = {4 + 3}/168 = 7/168$

Time taken by (A + B) working 8 hours daily

= $168/{7 × 8}$ = 3 days

Using Rule 21
If a man can do a certain work in '$d_1$' daysworking '$h_1$' hours in a days, while another man can do the same work in '$d_2$' days working '$h_2$' hours in a day. Whenthey work together everyday 'h' hours, then in how many days work will complete?
Required time = $[{({h_1d_1}) × ({h_2d_2})}/{h_1d_1 + h_2d_2}] 1/h$

Here, $h_1$ = 7 hours, $h_2$ = 7 hours, $d_1$ = 6 days, $d_2$ = 8 days, h = 8 hours

Required Time = $[{({7 × 6}) × ({7 × 8})}/{7 × 6 + 7 × 8}] × 1/8$

= ${42 × 56}/98 × 1/8 = 2352/98 × 1/8 = 24/8$ = 3 days

Question : 15 [SSC CGL Tier-1 2011]

A and B can complete a piece of work in 8 days, B and C can do it in 12 days, C and A can do it in 8 days. A, B and C together can complete it in

a) 7 days

b) 6 days

c) 4 days

d) 5 days

Answer: (b)

(A + B)’s 1 day’s work = $1/8$

(B + C)’s 1 day’s work = $1/12$

(C + A)’s 1 day’s work = $1/8$

On adding,

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

${3 + 2 + 3}/24 = 8/24 = 1/3$

(A + B + C)’s 1 day’s work = $1/6$

Hence, the work will be completed in 6 days.

Method 2 :

Time = ${2xyz}/{xy + yz + zx}$

(Here, x = 8, y = 12; z = 8)

= ${2 × 8 × 12 × 8}/{96 + 96 + 64}$

${2 × 8 × 12 × 8}/256$ = 6 days.

Using Rule 5,

Time taken = ${2 × 8 × 12 × 8}/{8 × 12 + 12 × 8 + 8 × 8}$

= ${16 × 96}/{96 + 96 + 64} = {16 × 96}/256$ = 6 days

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