Model 1 Basics On Time & Work Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

(A + B)’s 1 hour’s work = $2/9$ .....(i)

(B + C)’s 1 hour’s work = $1/3$ ......(ii)

(C + A)’s 1 hour’s work = $4/9$ .....(iii)

Adding all three equations,

2 (A + B + C)’s 1 hour’s work = $2/9 + 1/3 + 4/9$

${2 + 3 + 4}/9$ = 1

A, B and C together will complete the work in 2 hours.

Using Rule 5,

Time taken = ${2 × 9/2 × 3 × 9/4}/{9/2 × 3 + 3 × 9/4 + 9/2 × 9/4}$

= ${{18 × 27}/8}/{27/2 + 27/4 + 81/8}$

= ${18 × 27}/8 × 8/({108 + 54 + 81})$

= ${18 × 27}/243$ = 2 hours

Answer: (d)

According to the question

Work done by A and B together in one day = $1/10$ part

Work done by B and C together in one day = $1/15$ part

Work done by C and A together in one day = $1/20$ part

So, A + B = $1/10$ ....(I)

B + C = $1/15$ ...(II)

C + A = $1/20$ ....(III)

Adding I, II, III, we get

2 (A + B + C) = $1/10 + 1/15 + 1/20$

2 (A + B + C) = ${6 + 4 + 3}/60 = 13/60$

A + B + C = $13/120$ ....(IV)

Putting the value of eqn. (I) in eqn. (IV)

$1/10 + C =13/120$

C = $13/120 - 1/10 = {13 - 12}/120 = 1/120$

Work done in 1 day by C is $1/120$ part

Hence, C will finish the whole work in 120 days

Time Taken by C= ${2xyz}/{xy - yz + zx}$

= ${2 × 10 × 15 × 20}/{10 × 15 - 15 × 20 + 20 × 10 }$

= $6000/{150 - 300 + 200} = 6000/50$ = 120 days

Answer: (c)

(A + B)’s 1 day’s work = $1/18$

(B + C)’s 1 day’s work = $1/24$

(A + C)’s 1 day’s work = $1/36$

Adding all three,

2 (A + B + C)’s 1 day’s work= $1/18 + 1/24 + 1/36$

= ${4 + 3 + 2}/72 = 1/8$

(A + B + C)’ 1 day’s work = $1/16$

A, B and C together will complete the work in 16 days.

Using Rule 5,

Total time taken = ${2 × 18 × 24 × 36}/{18 × 24 +24 × 36 + 36 × 18}$

= ${36 × 24 × 36}/{432 + 864 + 648}$

= $31104/1944$ = 16 days

Answer: (a)

(A + B)’s 1 day’s work = $1/12$

(B + C)’s 1 day’s work = $1/15$

(C + A)’s 1 day’s work = $1/20$

On adding,

2 (A + B + C)’s 1 day's work = $1/12 + 1/15 + 1/20$

= ${5 + 4 + 3}/60 = 1/5$

(A+B+C)’s 1 day’s work = $1/10$

B’s 1 day’s work = $1/10 - 1/20 = {2 - 1}/20 = 1/20$

B alone can do the work in 20 days.

Using Rule 19,

B alone can do in = ${2 × 12 × 15 × 20}/{-12 × 15 + 15 × 20 + 20 × 12}$

= ${24 × 300}/{-180 + 300 + 240} = {24 × 300}/360$ = 20 days

Answer: (c)

(A + B)’s 1 day’s work = $1/15$

B’s 1 day’s work = $1/20$

A’s 1 day’s work = $1/15 - 1/20 = {4 - 3}/60 = 1/60$

A alone will do the work in 60 days.

Using Rule 4,

A alone do in = ${15 × 20}/{20 - 15}$

= ${15 × 20}/5$ = 60 days

Answer: (c)

A’s 1 day’s work = $1/12$

(A+B)’s 1 day’s work = $1/8$

B’s 1 day’s work =$1/8 - 1/12 = {3 - 2}/24 = 1/24$

B alone can do the work in 24 days.

Using Rule 4,

Time taken by B = ${12 × 8}/{12 - 8}$ = 24 days