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 = $1/72$

(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: (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 = $1/20$

(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

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 = $1/90$

On adding all three

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

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

(A+B+C)’s 1 day’s work = $1/60$

(A+B+C) will do the work in 60 days.

Using Rule 5,

Time taken = ${2 × 72 × 120 × 90}/{72 × 120 + 120 × 90 + 72 × 90}$

= $1555200/{8640 + 10800 + 6480}$

= $1555200/25920$ = 60 days

Answer: (b)

A’s 1 day’s work = $1/24$

B’s 1 day’s work = $1/6$

C’s 1 day’s work = $1/12$

(A + B + C)’s 1 day’s work

=$1/24 + 1/6 + 1/12 = {1 + 4 + 2}/24 = 7/24$

The work will be completed by them in $24/7$ i.e., 3$3/7$ days

Time taken = ${24 × 6 × 12}/{24 × 6 + 6 × 12 + 24 × 12}$

= $1728/{144 + 72 + 288}$

= $1728/504 = 24/7 = 3{3}/7$ days

Answer: (c)

(A+B)’s 1 day’s work = $1/10$

(B + C)’s 1 day’s work = $1/12$

(C + A)’s 1 day’s work = $1/15$

On adding all three,

2(A + B + C)’s 1 day’s work = $1/10 + 1/12 + 1/15$

= ${6 + 5 + 4}/60 = 15/60 = 1/44$

(A + B + C)’s 1 day’s work = $1/8$

A’s 1 day’s work = $1/8 - 1/12$

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

A will complete the work in 24 days.

Using Rule 19,

A alone can do in = ${2 × x × y × z}/{xy + yz - zx}$

= ${2 × 10 × 12 × 15}/{10 × 12 + 12 × 15 - 15 × 10}$

= $3600/{120 + 180 - 150}$

= $3600/150$ = 24 days