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

Question : 21 [SSC CPO S.I.2005]

A and B together can complete a piece of work in 72 days, B and C together can complete it in 120 days, and A and C together in 90 days. In what time can A alone complete the work ?

a) 150 days

b) 120 days

c) 80 days

d) 100 days

Answer: (b)

(A + B)’s 1 day’s work = $1/72$

(B + C)’s 1 day’s work = $1/120$

(C + A)’s 1 day’s work = $1/90$

Adding all three,

2(A + B + C)’s 1 day’s work = $1/72 + 1/120 + 1/90$

= ${5 + 3 + 4}/360 = 12/360 = 1/30$

(A + B + C)’s 1 day’s work = $1/60$

Now, A’s 1 day’s work = (A + B + C)’s 1 day’s work - (B + C)’s 1 day’s work

= $1/60 - 1/120 = {2 - 1}/120 = 1/120$

A alone can complete the work in 120 days.

Using Rule 19,

A alone can do in

= ${2 × 72 × 120 × 90}/{72 × 120 + 120 × 90}$ - 72 × 90

= ${2 × 72 × 120 × 90}/{8640 + 10800}$ - 6480

= ${144 × 10800}/12960$ = 120 days

Question : 22 [SSC CPO S.I.2004]

A and B together can do a piece of work in 10 days. A alone can do it in 30 days. The time in which B alone can do it is

a) 20 days

b) 15 days

c) 10 days

d) 12 days

Answer: (b)

(A + B)’s 1 day’s work = $1/10$

A’s 1 day’s work = $1/30$

B’s 1 day’s work = $1/10 - 1/30$

= ${3 - 1}/30 = 2/30 = 1/15$

Hence, B, alone can complete the work in 15 days.

Using Rule 4
If A alone can do a certain work in 'x' days and A and B together can do the same work in 'y' days, then B alone can do the same work in $({xy}/{x - y})$ days.

Time taken by B = ${30 × 10}/{30 - 10}$ = 15 days

Question : 23 [SSC CHSL 2011]

If A and B together can finish a piece of work in 20 days, B and C in 10 days and C and A in 12 days, then A, B, C jointly can finish the same work in

a) $7/60$ days

b) 8$4/7$ days

c) 4$2/7$ days

d) 30 days

Answer: (b)

(A + B)’s 1 day’s work = $1/20$

(B + C)’s 1 day’s work = $1/10$

(C + A)’s 1 day’s work = $1/12$

On adding all three,

2 (A + B + C)’s 1 day’s work = $1/20 + 1/10 + 1/12$

= ${3 + 6 + 5}/60 = 14/60 = 7/30$

(A + B + C)’s 1 day’s work = $7/60$

Hence, the work will be completed in $60/7 = 8{4}/7$ days.

Using Rule 5,

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

= ${2 × 20 × 10 × 12}/{20 × 10 + 10 × 12 + 12 × 20}$

= $4800/{200 + 120 + 240}$

= $4800/560 = 60/7 = 8{4}/7$ days

Question : 24 [SSC DEO 2008]

A and B together can do a piece of work in 5 days and A alone can do it in 8 days. B alone can do the same piece of work in

a) 16$4/5$ days

b) 13$1/3$ days

c) 11$1/3$ days

d) 12$3/5$ days

Answer: (b)

(A + B)’s 1 day’s work = $1/5$

A’s 1 day’s work = $1/8$

B’s 1 day’s work = $1/5 - 1/8$

= ${8 - 5}/40 = 3/40$

B alone will complete the work in $40/3 = 13{1}/3$ days.

Using Rule 4,

Time taken by B = ${5 × 8}/{8 - 5}$

= $40/3 = 13{1}/3$ days

Question : 25 [SSC MTS 2011]

A and B can do a piece of work in 8 days, B and C can do it in 24 days, while C and A can do it in 8$4/7$ days. In how many days can C do it alone?

a) 10 days

b) 30 days

c) 60 days

d) 40 days

Answer: (c)

(A + B)’s 1 day’s work = $1/8$

(B + C)’s 1 day’s work = $1/24$

(C + A)’s 1 day’s work = $7/60$

On adding all three,

2 (A + B + C)’s 1 day’s work = $1/8 + 1/24 + 7/60$

= ${15 + 5 + 14}/120 = 34/120$

(A + B + C)’s 1 day’s work = $17/120$

C’s 1 day’s work

= $17/120 - 1/8 = {17 - 15}/120 = 1/60$

C alone will complete the work in 60 days.

Using Rule 19,

C alone can do in= ${2xyz}/{xy - yz + zx}$

= ${2 × 8 × 24 × 60/7}/{8 × 24 - 24 × 60/7 + 60/7 × 8$

= ${23040/7}/{192 - 1440/7 + 480/7}$

= ${23040/7}/{{1344 - 1440 + 480}/7}$

= $23040/7 × 7/384$ = 60 days

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