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

Answer: (d)

(A + B)’s 1 day’s work = $1/72$

(B + C)’s 1 day’s work = $1/120$

(C + A)’s 1 day’s work = $1/90$

On adding all three,

2 (A + B + C)’s 1 day’s work

= $1/72 + 1/120 + 1/90 = {5 + 3 + 4}/360 = 1/30$

(A + B + C)’s 1 day’s work = $1/60$

(A + B + C)’s 3 days’ work = $3/60 = 1/20$

Answer: (a)

Time taken by P in completing 1 work

= 10 × 4 = 40 days

Time taken by Q in completing 1 work

= ${15 × 5}/2 = 75/2$ days

Time taken by R in completing 1 work

= 13 × 3 = 39 days

Time taken by S in completing 1 work

= 7 × 6 = 42 days

Clearly, Q took the least time i.e. $75/2$ or 37${1}/2$ days.

Answer: (b)

Using Rule 2,

Let B completes the work in x days.

Work done by A in ${3x}/4$ days = $1/2$

Time taken by A in completing the work = $2 × {3x}/4 = {3x}/2$ days

(A + B)’s 1 day’s work

= $1/x + 2/{3x} = {3 + 2}/{3x} = 5/{3x}$

$5/{3x} = 1/18$ ⇒ 3x = 90 ⇒ x = 30

Hence, time taken by B in completing the work = 30 days

Answer: (a)

A can do a work in 12 days.

B is 60% more efficient than A.

Time taken by B = $(100/160 × 12)$ days

= $15/2 = 7{1}/2$ days

Answer: (c)

Dhiru digs $1/a$ part of field in 20 hours.

Dhiru digs 1 part of field in 20a hours.

= $1/60 - 1/{20a} = {a - 3}/{60a}$

Part of field dug by Kaku in 1 hour

= ${20(a - 3)}/{60a} ={a - 3}/{3a}$

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