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

Answer: (b)

Using Rule 2,

A can do the whole work in ${20 × 5}/4 = 25$ days

Remaining work = $1 - 4/5 = 1/5$

(A + B)’s 1 day’s work = $1/15$

and A’s 1 day’s work = $1/25$

B’s 1 day’s work

= $1/15 - 1/25 = {5 - 3}/75 = 2/75$

B can finish the work in $75/2$ days

i.e., 37$1/2$ days

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: (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

Answer: (c)

Using Rule 2,

A does $7/8$ work in 28 days.

A will complete the work in

$28 × 8/7$ = 32 days.

B does $5/6$ work in 20 days.

B will complete the work in

${20 × 6}/5$ = 24 days

(A + B)’s 1 day’s work

= $1/32 + 1/24 = {3 + 4}/96 = 7/96$

Required time = $96/7 =13{5}/7$ days