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 = $1/10$

(B + C)’s 1 day’s work = $1/6$

(C + A)’s 1 day’s work = $1/12$

Adding all three

2 (A + B + C)’s 1 day’s work = $1/10 + 1/6 + 1/12$

${6 + 10 + 5}/60 = 21/60 = 7/20$

(A + B + C)’s 1 day’s work = $7/40$

All three together will complete the work in $40/7 = 5{5}/7$ = days

Using Rule 5,

Time taken = ${2 × 10 × 6 × 12}/{10 × 6 + 6 × 12 + 12 × 10}$

= $1440/{60 + 72 + 120}$

= $1440/252 = 40/7 = 5{5}/7$ days

Answer: (d)

Work done by (A + B + C) in 1 minute = $1/30$

Work done by (A + B) in 1 minute = $1/50$

Work done by C alone in 1 minute = $1/30 - 1/50$

= ${5 - 3}/150 = 2/150 = 1/75$

C alone will complete the work in 75 minutes.

Using Rule 4,

C alone can do in = ${xy}/{x - y}$

= ${50 × 30}/{50 - 30}$ = 75 minutes

Answer: (b)

A’s 1 hour’s work = $1/4$

(B + C)’s 1 hour’s work = $1/3$

(A + C)’s 1 hour’s work = $1/2$

C’s 1 hour’s work

= $1/2 - 1/4 = {2 - 1}/4 = 1/4$

and B’s 1 hour’s work

= $1/3 - 1/4 = {4 - 3}/12 = 1/12$

Hence, B alone can do the work in 12 hours.

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.

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

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