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

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: (c)

Using Rule 2,

Ratio of efficiency of A and B = 3 : 2

Ratio of time taken = 2 : 3

Time taken by A

= $2/3$ × 18 = 12 days

(A + B)’s 1 day’s work

= $1/12 + 1/18 = {3 + 2}/36 = 5/36$

Required time = $36/5 = 7{1}/5$ days

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: (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 = $1 - 3/8 = 5/8$

Answer: (a)

Using Rule 2,

If B completes a work in x days,

A will complete the same in ${2x}/3$ days.

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

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

2x = 50 ⇒ x = 25 days

Answer: (a)

Using Rule 2,

x does $1/4$ work in 6 days

x does 1 work in 24 days

Similarly,

y does $3/4$ work in12 days

y does 1 work in ${12 × 4}/3$ = 16 days

(x + y)’s 1 day’s work

= $1/24 + 1/16 = {2 + 3}/48 = 5/48$

Required time = $48/5 = 9{3}/5$ days