Model 3 Man leaves & joins Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (c)

B’s 1 day's work

= $1/12 - 1/20 = {5 - 3}/60 = 1/30$

B's $1/2$ day’s work = $1/60$

(A + B)'s 1 day's work

= $1/20 + 1/60 = {3 + 1}/60 = 1/15$

[Since, B works for half day daily]

Hence, the work will be completed in 15 days.

Answer: (d)

Let A and B worked together for x days

According to the question,

Part of work done by A for (x + 10) days

+ part of work done by B for x days = 1

${x + 10}/20 + x/30$ = 1

${3x + 30 + 2x}/60 = 1$

5x + 30 = 60

5x = 30 ⇒ x = $30/5$ = 6 days

Here, m =20, n= 30, p = x and time taken by A alone = 10

10 = ${mn - p(m + n)}/n$

10 = ${30 × 20 - x(30 + 20)}/30$

300 = 600 - x 50

50x = 300 x = 6

B worked for 6 days

Answer: (d)

Work done in first two days

= ${2/30 + 1/20 + 1/10 = 1/15 + 1/20 + 1/10$

= ${4 + 3 + 6}/60 = 13/60$

Work done in first 8 days = $52/60$

Remaining work

= $1 - 52/60 = 8/60 = 2/15$

(A + B)’s 1 day’s work

= $1/30 + 1/20 = {2 + 3}/60 = 1/12$

Remaining work = $2/15 - 1/12$

= ${8 - 5}/60 = 3/60 = 1/20$

(A + C)’s 1 day’s work

= $1/30 + 1/10 = {1 + 3}/30 = 2/15$

Time taken = $1/20 × 15/2 = 3/8$ day

Total time = $9 + 3/8 = 9{3}/8$ days

Answer: (a)

(A + B)’s 1 day’s work

= $(1/45 + 1/40) = {8 + 9}/360 = 17/360$

Work done by B in 23 days

= $1/40 × 23 = 23/40$

Remaining work = $1 - 23/40 = 17/40$

Now, $17/360$ work was done by (A + B) in 1 day

$17/40$ work was done by (A + B) in $1 × 360/17 × 17/40$ = 9 days.

Hence, A left after 9 days.

Here, x = 45, y = 40, a = 23

Required time t= $\text"(y - a)"/\text"(x + y)" × x$

t = ${(40 - 23) × 45}/{45 + 40} = {17 × 45}/85$

t = 9 days

Answer: (b)

Let the work be completed in x days.

According to the question,

${x - 5}/10 + {x - 3}/12 + x/15$ = 1

${6x - 30 + 5x - 15 + 4x}/60$ = 1

15x - 45 = 60

15x = 105 ⇒ x = $105/15$ = 7

Hence, the work will be completed in 7 days.

Answer: (a)

(A+B)’s 1 day’s work = $1/30$

(A + B)’s 20 day’s work = $20/30 = 2/3$

Remaining work = $1 - 2/3 = 1/3$

Now, $1/3$ part of work is done by A in 20 days.

Whole work will be done by A alone in 20 × 3 = 60 days.