**Time and work practice set 1**

**Example 1:** Two boy alone or three girl alone can complete a piece of work in 4 days. In how many days can 1 girl and 1 boy together complete the same piece of work ?

**Solution :**

2Boy = 3Girl

1 Boy = 3/2 girl

1girl + 1 boy

1girl + 3/2 girl

= 5/2 girl

M1D1 = M2D2

3X4 = 5X?/2

? = 24/5

**Example 2:** Rajan can do a piece of work in 10 days and Rahim can do same work in 15 days. if sujay joins them, who can complete the same work in 30 days, how long will they take to complete the work ?

**Solution :**

10 x 15 x 30 / 10 x 15 + 10 x 30 + 15 x 30 = 10 x 15 x 30 / 900 = 5 days.

**Example 3:** 8 boy can complete a piece of work in 20 days. 8 girl can complete the same work in 32 days, how many days will 5 boy and 8 girl together complete the same work ?

**Solution :**

Required days = 5 / 8×20 + 8 / 32×8 = 2/32 = 16 days

**Example 4:** P and Q can do a piece of work in 12 days, Q and R in 15 days, R and P in 20 days. How long will they take separately to do the same piece of work ?

**Solution :**

all can do the work in 2(P+Q+R) = 12x15x20/12×15+12×20+15×20 = 5 days.

P can do the piece of work in 10×15/15-10 = 30 days.

Q can do the piece of work in 10×20/20-10 = 20 days.

R can do the piece of work in 10×12/12-10 = 60 days.

**Example 5:** If 3 boy or 4 girl can do a piece of work in 43 days, how long will 7 boy and 5 girl take to complete the work?

**Solution :** 43x3x4/7×4+5×3 = 12 days.

**Example 6:** Pradip is thrice as fast as bijoy, and is therefore able to finish a work in 60 days less than bijoy. Find the time in which they can do it working together

**Solution :**

pradip does the work in 1 day and bijoy does it in 3 days.

So, difference is 60 days, therefore pradip does the work in 30 days and bijoy in 90 days.

they both work together in,

30×90/30+90 = 22.5days

**Example 7:** A certain number of women can do a work in 80 days. If there were 10 women more it could be finished in 20 days less. How many women are there ?

**Solution :** x man do the work in 80 and (x+10) women do the work in (80-20)=60 days

80x=60(x+8)

x=60×10/20=30 women

**Example 8:** 6 boy can complete a piece of work in 12 days. 8 girl can complete the same piece of work in 18 days whereas 18 children can complete the piece of work in 10 days. 4 boy, 12 girl and 20 children work together for 2 days. If only boy were to complete the remaining work in 1 day, how many men would be required totally ?

**Solution :** Time taken by 4 boy to complete the work = 6×12 = 4xX

X = 18 days

Time taken by 12 girl to complete the work = 8×18 = 12xX

X = 12 days

Time taken by 20 children to complete the work = 18×10 = 20xX

X=9 days.

In 2 days 4 boy,12 girls, 20 children work done

2(1/18 + 1/12 + 1/9) = 1/2 part

due work = (1-1/2)

So, required boy to complete the work due work

6×12/1 = X x 1/1/2

X = 36

Example 9: 8 boy can complete a piece of work in 20days. 8 girl can complete the same work in 32 days, how many days will 5 boy and 8 girl together complete the same work ?

Solution :

=5/8×20 + 8/8×32

=2/32

=16 days

Example 10: A certain number of women complete a work in 160 days. If there were 18 women more, the work could be finished in 20 days less. How many women were originally there ?

Solution :Original number of women = 18 x(160-20)/20 = 126

Example 11: A contractor take a contract for road 12 km long in 350 days and take 45 labour.After 200 days he find that only 4.5 km of the road has been completed. Find the number of extra labour he must take to finish the work in time ?

Solution :M1 D1 W2 = M2 D2 W1

45X200X7.5 = M2X150X4.5

M2=45X200X7.5/150X4.5=100

So required number of labour to be added is = 100-45=55

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