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

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

Question : 6 [SSC CGL Prelim 2002]

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 : 7 [SSC CISF ASI 2010]

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 : 8 [SSC CGL Prelim 2005]

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 : 9 [SSC CHSL 2011]

A and B together can complete a work in 8 days and B and C together in 12 days. All of the three together can complete the work in 6 days. In how much time will A and C together complete the work ?

a) 20 days

b) 12 days

c) 8 days

d) 10 days

Let A and C complete the work in x 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/x\$

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

2(A + B + C)’s 1 day’s work = \${3x + 2x + 24}/{24x}\$

(A + B + C)’s 1 day’s work = \${5x + 24}/{24x × 2}\$

According to the question,

(A + B + C)’s 1 day’s work = \$1/6\$

\$1/6 = {5x + 24}/{48x}\$

30x + 144 = 48x ⇒ x = \$144/18\$ = 8 days.

Using Rule 5,

Let the time taken by A and C bc x days

Total time taken = \${2 × 8 × 12 × x}/{8 × 12 + 12 × x + 8 × x}\$

6 = \${192x}/{96 +20x}\$

576 + 120x = 192x

72x = 576 ⇒ x = 8

Time taken by A and C is 8 days.

Question : 10 [SSC CGL Prelim 2000]

A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work?

a) 3 days

b) 3.6 days

c) 7.5 days

d) 5.4 days

According to question,

A can finish the whole work in 6 days.

A’s one day’s work = \$1/6\$

Similarly, B’s one day’s work = \$1/9\$

(A + B)’s one day’s work

= \$(1/6 + 1/9) = ({3 + 2}/18) = 5/18\$

Therefore, (A + B)’s can finish the

whole work in \$18/5\$ days i.e., 3.6 days.

Using Rule 2
If A completes a piece of work in 'x' days, and B completes the same work in 'y' days, then,
Work done by A in 1 day = \$1/x\$, Work done by B in 1 day = \$1/y\$
Work done by A and B in 1 day = \$1/x + 1/y = {x + y}/{xy}\$
Total time taken to complete the work by A and B both = \$({xy}/{x + y})\$

Time taken = \${6 × 9}/{9 + 6} = 54/15\$ = 3.6 days

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