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

Answer: (d)

B completes $1/3$ work in 12 days.

B will complete 1 work in 12 × 3 = 36 days.

B’s 1 day’s work = $1/36$

(A + B)’s 1 day’s work = $1/24$

A’s 1 day’s work = $1/24 - 1/36$

= ${3 - 2}/72 = 1/72$

Time taken by A in doing 1work = 72 days

∴ Remaining work

= $1 - 1/3 = 2/3$

Time taken by A in doing $2/3$ work

= $2/3$ × 72 = 48 days

Answer: (d)

Using Rule 1,

${M_1D_1}/W_1= {M_2D_2}/W_2$

$10/{2/3} = D_2/{3/5}$

$30/2 = {5D_2}/3$

$D_2 = 30/2 × 3/5$ = 9 days

Answer: (c)

Time taken by A and B = x hours (let).

According to the question,

Time taken by A alone

= (x + 8) hours.

Time taken by B alone

= $(x + 9/2)$ hours.

$1/{x + 8} + 1/{x + {9/2}} = 1/x$

$1/{x + 8} + 2/{2x + 9} =1/x$

${2x + 9 + 2x + 16}/{(x + 8)(2x + 9)} = 1/x$

${4x + 25}/{2x^2 + 16x + 9x + 72} = 1/x$

$4x^2 + 25x = 2x^2 + 25x + 72$

$2x^2 = 72 ⇒ x^2 = 72/2 = 36$

x = $√{36}$ = 6 hours

Answer: (a)

Using Rule 1,

∴ ${30 : 60}/{3/4 : 1/4}]$ : : 60 : x

$30 × 3/4 × x = 60 × 1/4 × 60$

$x = {60 × 60}/{30 × 3}$ = 40

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)

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.