Model 5  Split & Fraction of work Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (b)

Let time taken by A alone in doing work be x days.

Time taken by B alone = 3x days

A and B together finish $2/5$ work in 9 days.

TIme taken by A and B in doing whole work

= ${9 × 5}/2 = 45/2$ days

$1/x + 1/{3x} = 2/45$

${3 + 1}/{3x} = 2/45$

$4/{3x} = 2/45$ ⇒ 2 × 3x = 4 × 45

$x = {4 × 45}/{2 × 3}$ = 30 days

Time taken by B = 3x days = 3 × 30 = 90 days

Here, n = 3 and D = ${9 × 5}/2 = 45/2$ days

(Time taken to finish whole work)

Time taken by B = (n + 1)D

= (3 + 1) × $45/2$ = 90 days

Answer: (b)

A’s work per day = $1/15$

B’s work per day = $1/20$

(A+ B)’s work per day

= $1/15 + 1/20 = {4 + 3}/60 = 7/60$

(A + B)’s work in 4 days

= $4 × 7/60 = 7/15$

Left work = $1 - 7/15 = {15 - 7}/15 = 8/15$

Answer: (a)

Part of work done by A and B = $19/23$

Part of work done by C = $1 - 19/23 = 4/23$

Part of work done by B and C = $8/23$

Part of work done by B

= $8/23 - 4/23 = 4/23$

Part of work done by A

= $19/23 - 4/23 = 15/23$

Ratio of the shares of wages of A, B and C

= $15/23 : 4/23 : 4/23$ = 15 : 4 : 4

A’s share = $15/23$ × 5290 = Rs.3450

Answer: (d)

A does $1/3$ rd part of work in 5 days.

A will do 1 work in 5 × 3 = 15 days.

B does $2/5$ th of work in 10 days.

B will do 1 work in ${10 × 5}/2$ = 25 days.

(A + B)’s 1 day’s work

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

∴ Required time

= $75/8 = 9{3}/8$ days

Answer: (d)

Using basics of Rule 2,

Time taken by A to complete the work

= ${4 × 3}/2$ = 6 days

Time taken by B to complete the work

= ${6 × 5}/3$ = 10 days

(A + B)’s 1 day’s work

= $1/6 + 1/10 = {5 + 3}/30 = 8/30 = 4/15$

A and B together will complete the work in

$15/4 = 3{3}/4$ days.