# Practice Basics On Time And Work - Quantitative Aptitude Online Quiz (Set-1) For All Competitive Exams

#### Q-1) A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work?

(a)

(b)

(c)

(d)

**Explanation:**

According to question,

A can finish the whole work in 6 days.

A’s one day’s work = $1/6$

Similarly, B’s one day’s work = $1/9$

(A + B)’s one day’s work

= $(1/6 + 1/9) = ({3 + 2}/18) = 5/18$

Therefore, (A + B)’s can finish the

whole work in $18/5$ days i.e., 3.6 days.

**Using Rule 2**

If A completes a piece of work in 'x' days, and B completes the same work in 'y' days, then,

Work done by A in 1 day = $1/x$, Work done by B in 1 day = $1/y$

Work done by A and B in 1 day = $1/x + 1/y = {x + y}/{xy}$

Total time taken to complete the work by A and B both = $({xy}/{x + y})$

Time taken = ${6 × 9}/{9 + 6} = 54/15$ = 3.6 days

#### Q-2) A and B can complete a piece of work in 8 days, B and C can do it in 12 days, C and A can do it in 8 days. A, B and C together can complete it in

(a)

(b)

(c)

(d)

**Explanation:**

(A + B)’s 1 day’s work = $1/8$

(B + C)’s 1 day’s work = $1/12$

(C + A)’s 1 day’s work = $1/8$

On adding,

2 (A + B + C)’s 1 day’s work = $1/8 + 1/12 + 1/8$

${3 + 2 + 3}/24 = 8/24 = 1/3$

(A + B + C)’s 1 day’s work = $1/6$

Hence, the work will be completed in 6 days.

Method 2 :

Time = ${2xyz}/{xy + yz + zx}$

(Here, x = 8, y = 12; z = 8)

= ${2 × 8 × 12 × 8}/{96 + 96 + 64}$

${2 × 8 × 12 × 8}/256$ = 6 days.

**Using Rule 5,**

Time taken = ${2 × 8 × 12 × 8}/{8 × 12 + 12 × 8 + 8 × 8}$

= ${16 × 96}/{96 + 96 + 64} = {16 × 96}/256$ = 6 days

#### Q-3) A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in

(a)

(b)

(c)

(d)

**Explanation:**

A’s 1 day’s work = $1/24$

B’s 1 day’s work = $1/6$

C’s 1 day’s work = $1/12$

(A + B + C)’s 1 day’s work

=$1/24 + 1/6 + 1/12 = {1 + 4 + 2}/24 = 7/24$

The work will be completed by them in $24/7$ i.e., 3$3/7$ days

**Using Rule 3**

If A can do a work in 'x' days, B can do the same work in 'y' days, C can do the same work in 'z' days then, total time taken by A, B and C to complete the work together = $1/{1/x + 1/y + 1/z} = {xyz}/{xy + yz + zx}$and

If workers are more than 3 then total time taken by A, B, C ...... so on to complete the work together = $1/{1/x + 1/y + 1/z + ...}$

Time taken = ${24 × 6 × 12}/{24 × 6 + 6 × 12 + 24 × 12}$

= $1728/{144 + 72 + 288}$

= $1728/504 = 24/7 = 3{3}/7$ days

#### Q-4) A, B and C individually can do a work in 10 days, 12 days and 15 days respectively. If they start working together, then the number of days required to finish the work is

(a)

(b)

(c)

(d)

**Explanation:**

Work done by A, B and C in 1 day

= $1/10 + 1/12 + 1/15 = {6 + 5 + 4}/60$

= $15/60 = 1/4$

Required time = 4 days

**Using Rule 3,**

Time Taken = ${xyz}/{xy + yz + zx}$

= ${10 × 12 × 15}/{10 × 12 + 12 × 15 + 15 × 10}$

= $1800/{120 + 180 + 150}$

= $1800/450$ = 4 days

#### Q-5) A alone can complete a work in 12 days. A and B together can complete it in 8 days. How long will B alone take to complete the work ?

(a)

(b)

(c)

(d)

**Explanation:**

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

#### Q-6) If A and B together can complete a piece of work in 15 days and B alone in 20 days, in how many days can A alone complete the work ?

(a)

(b)

(c)

(d)

**Explanation:**

(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

#### Q-7) If A and B together can complete a work in 12 days, B and C together in 15 days and C and A together in 20 days, then B alone can complete the work in

(a)

(b)

(c)

(d)

**Explanation:**

(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

#### Q-8) A and B can do a piece of work in 12 days, B and C in 8 days and C and A in 6 days. How long would B take to do the same work alone ?

(a)

(b)

(c)

(d)

**Explanation:**

(A + B)'s 1 day's work = $1/12$ ...(i)

(B + C)'s 1 day's work = $1/8$ ...(ii)

(C + A)'s 1 day's work = $1/6$ ...(iii)

On adding,

2(A + B + C)'s 1 day's work = $1/12 + 1/8 + 1/6$

= ${2 + 3 + 4}/24 = 9/24$

(A+ B + C)'s 1 day’s work = $9/{24 × 2} = 9/48$ ...(iv)

On, subtracting (iii) from (iv),

B’s 1 day’s work = $9/48 - 1/6$

= ${9 - 8}/48 = 1/48$

B can complete the work in 48 days.

**Using Rule 19,**

B alone can do in = ${2 × 12 × 8 × 6}/{-12 × 8 + 8 × 6 + 6 × 12}$

= ${24 × 48}/{-96 + 48 + 72} = {24 × 48}/{-96 + 120}$

= ${24 × 48}/24$ = 48 days

#### Q-9) A and B can do a piece of work in 10 days, B and C in 15 days and C and A in 20 days. C alone can do the work in :

(a)

(b)

(c)

(d)

**Explanation:**

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

**Using Rule 19**

A and B can do a work in 'x' days, B and C can do the same work in 'y' days. C and A can do the same work in 'z' days. Then, all can do alone the work as following:

A alone can do in =${2xyz}/{xy + yz - zx}$days

B alone can do in =${2xyz}/{-xy + yz + zx}$days

C alone can do in =${2xyz}/{xy - yz + zx}$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

#### Q-10) A and B together can complete a piece of work in 18 days, B and C in 24 days and A and C in 36 days. In how many days, will all of them together complete the work ?

(a)

(b)

(c)

(d)

**Explanation:**

(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