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

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

Answer: (d)

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

Answer: (c)

(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 = $1/36$

Adding all three,

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

Answer: (b)

(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)

On adding,

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

Answer: (c)

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

Answer: (b)

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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