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

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: (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: (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: (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