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

Answer: (b)

(P + Q)’s 1 day’s work = $1/12$ ...(i)

(Q + R)’s 1 day’s work = $1/15$ ...(ii)

(R + P)’s 1 day’s work = $1/20$ ...(iii)

Adding all three equations,

2 (P + Q + R)’s 1 day’s work = $1/12 + 1/15 + 1/20$

${5 + 4 + 3}/60 = 12/60 = 1/5$

(P + Q + R)’s 1 day’s work = $1/10$ ...(iv)

P’s 1 day’s work = $1/10 - 1/15 = {3 - 2}/30 = 1/30$

P alone will complete the work in 30 days.

Answer: (c)

According to question,

10 men’s one day’s work = $1/12$

1 man one day’s work =$1/{12 × 10} = 1/120$

Similarly, 1 woman one day’s work = $1/{6 × 10} = 1/60$

(1 man + 1 woman)’s one day’s work = $1/120 + 1/60$

= ${1 + 2}/120 = 3/120 = 1/40$

(10 men + 10 women)’s one day’s work = $10/40 = 1/4$

Therefore, both the teams can finish the whole work in 4 days.

Answer: (b)

(A + B)'s 1 day's work = $1/10$ ... (i)

(B + C)'s 1 day’s work = $1/12$ ... (ii)

(C + A)’s 1 day’s work = $1/15$ ... (iii)

On adding all these,

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

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

(A + B + C)’s 1 day’s work = $1/8$ … (iv)

C’s 1 day’s work = $1/8 - 1/10 = {5 - 4}/40 = 1/40$

C will finish the work in 40 days.

Using Rule 19,

C alone can do in = ${2 × 10 × 12 × 15}/{10 × 12 - 12 × 15 + 10 × 15}$

= ${240 × 15}/{120 - 180 + 150} = {240 × 15}/90$ = 40 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: (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)

(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