Model 1 Basics on Time & Work Section-Wise Topic Notes With Detailed Explanation And Example Questions

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

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

Answer: (b)

Work done by A, B and C in 1 day

= $1/10 + 1/12 + 1/15 = {6 + 5 + 4}/60$

= $15/60 = 1/4$

Required time = 4 days

Using Rule 3,

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

= ${10 × 12 × 15}/{10 × 12 + 12 × 15 + 15 × 10}$

= $1800/{120 + 180 + 150}$

= $1800/450$ = 4 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.

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

Answer: (d)

(A + B)’s 1 day’s work = $1/18$

(B + C)’s 1 day’s work = $1/9$

(A + C)’s 1 day’s work = $1/12$

Adding all the above three,

2 (A + B + C)’s 1 day’s work = $1/18 + 1/9 + 1/12$

= ${2 + 4 + 3}/36 = 9/36 = 1/4$

(A + B + C)’s 1 day’s work = $1/8$

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

= $1/8 - 1/12 = {3 - 2}/24 = 1/24$

Hence, B alone can do the work in 24 days.

Using Rule 19,

B alone can do in = ${2 × 18 × 9 × 12}/{-18 × 9 + 12 × 9 + 12 × 18}$

= ${36 × 108}/{-162 + 108 + 216} = {36 × 108}/162$ = 24 days