Model 5  Split & Fraction of work Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (c)

According to the question,

John does $1/2$ work in 3 hours.

Time taken by John in doing whole work = 6 hours

Joe does $1/8$ work in 1 hour.

Time taken by Joe in doing whole work = 8 hours

Remaining work

= $1/2 - 1/8 = {4 - 1}/8 = 3/8$ parts

Time taken by George

= ${8 × 5}/3 = 40/3$ hours

Work done by all three in 1 hour

= $1/6 + 1/8 + 3/40$

= ${20 + 15 + 9}/120 = 44/120 = 11/30$

Required time = $30/11 = 2{8}/11$ hours

Answer: (c)

Using Rule 2

Work done by A and B in 1 day

= $1/10 + 1/20 = {2 + 1}/20 = 3/20$

(A + B)’s 5 days’ work

= ${5 × 3}/20 = 3/4$

Remaining work = $1 - 3/4 = 1/4$

Answer: (c)

Let the time taken by B in doing the work alone = x days

According to the question,

Time taken by A = $2 × {3x}/4 = {3x}/2$ days

$1/x + 1/{{3x}/2} = 1/18$

$1/x + 2/{3x} = 1/18$

${3 + 2}/{3x} = 1/18$

3x = 18 × 5

$x = {18 × 5}/3$ = 30 days

Answer: (a)

Using Rule 2,

Time taken by A alone in doing the work = 15 days

Time taken by B alone in doing the work

= ${10 × 5}/2$ = 25 days

(A + B)’s 1 day’s work

= $1/15 + 1/25 = {5 + 3}/75 = 8/75$

Hence, the work will be completed in $75/8 = 9{3}/8$ days.

Answer: (b)

Using basics of Rule 2,

Time taken by A to finish the work

= 5 × 6 = 30 days

Time taken by B to complete the work

= ${8 × 5}/2$ = 20 days

(A + B)'s 1 day’s work

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

Required time = 12 days

Answer: (b)

Using Rule 2,

(A + B)’s 5 days’ work = $5(1/20 + 1/40)$

= $5({2 + 1}/40) = 15/40 = 3/8$

Remaining work = $1 - 3/8 = 5/8$