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

#### TIME & WORK PRACTICE TEST [7 - EXERCISES]

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

(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\$

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

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

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

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

(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\$

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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