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

Answer: (c)

A can do $1/2$ work in 5 days.

A can do 1 work in 10 days

Similarly,

B can do 1 work in $5/3$ × 9 = 15 days.

C can do 1 work in 8 × $3/2$ = 12 days.

Now, A’s 1 day’s work = $1/10$

B’s 1 day’s work = $1/15$

C’s 1 day’s work = $1/12$

(A + B + C)’s 1 day’s work = $1/10 + 1/15 + 1/12$

= ${6 + 4 + 5}/60 = 15/60 = 1/4$

Hence, (A + B + C) together can complete the work in 4 days.

Answer: (a)

According to the question,

(4 × 8) men + (6 × 8) women ≡

(2 × 8) men + (9 × 8) women

4 men + 6 women ≡ 2 men + 9 women

(4 - 2) men ≡ (9 - 6) women

2 men ≡ 3 women

4 men + 6 women ≡ 12 women

$M_1D_1 = M_2D_2$

12 × 8 = 18 × $D_2$

$D_2 = {12 × 8}/18 = 16/3 = 5{1}/3$ days

Using Rule 11,

Here, $A_1$ = 4, $B_1$ = 6, $D_1$ = 8

$A_2$ = 2, $B_2$ = 9, $D_2$ = 8

$A_3$ = 0, $B_3$ = 18

Required time = ${D_1D_2(A_1B_2 - A_2B_1)}/{D_1(A_1B_3 - A_3B_1) - D_2(A_2B_3 - A_3 B_2)}$ days

= ${8 × 8(4 × 9 - 2 × 6)}/{8(4 × 18 - 0 × 6) - 8(2 × 18 - 0 × 9)}$

= ${64 × 24}/{8 × 72 - 36 × 8} = 192/36$

= $16/3 = 5{1}/3$ days

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: (d)

Since, P does $1/4$ th work in 10 days.

P will do 1 work in 10 × 4 = 40 days

Since, Q, does 40% part of work in 40 days

Q will do 100% work in

${40 × 100}/40$ = 100 days

Since, R, does $1/3$ rd work in 13 days.

R will do 1 work in 13 × 3 = 39 days

Answer: (d)

Using Rule 2,

The part of field cultivated by A in 1 day

= $2/{5 × 6} = 1/15$

The part of field cultivated by B in 1 day

= $1/{3 × 10} = 1/30$

The part of field cultivated by A and B together

= $1/15 + 1/30 = 3/30 = 1/10$

$4/5$ part of field cultivated by A and B together in

= ${4/5}/{1/10}$ days = ${4 × 10}/5 = 8$ days

Answer: (b)

Remaining work

= $1 - 37/100 = {100 - 37}/100 = 63/100$

Time taken by (A + B) in doing

$63/100$ part of work = 7 days

Time taken by them in doing whole work

= $100/63 × 7 = 100/9$ days

Respective ratio of time taken by

A and B in doing the work = 5 : 4

$1/{4x} + 1/{5x} = 9/100$

${5 + 4}/{20x} = 9/100$

20x = 100 ⇒ x = 5

Required time = 4 × 5 = 20 days