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
Example 12: Manoj can do a piece of work in 20 days and Sushil can do the same piece of work in 30 days. How long would they take to do it working together?
Solution :
20×30/20+30 = 12days
Example 13:Sahil, Sujay, Sam can do a piece of work in 8,16,32 days respectively.In what time will they altogether do it?
Solution :8x16x32/8×16+16×32+8×32 = 8x16x32/128+560+256 = 4096/944 = 4.33 days
Example 14:6 boys can complete a piece of work in 12 days. 8 girls can complete the same piece of work in 18 days whereas 18 childrens can complete the piece of work in 10 days. 4 boy, 12 girl and 20 children work together for 2 days. If only boy where to complete the remaining work in 1 day, how many boy would be required totally?
Solution : time taken 4 boy
= 6×12=4xX
X = 18
Time taken 12 girl
= 8×18 = 12 x X
X = 12days
Time taken 20 children
18 x 10 = 20 x X
X = 9
work by 2 days by 4 boy, 12 girl and 20 children
=2(1/18 + 1/12 + 1/9)
= 1/2 part
required boy to complete the work
6×12/1 = X x 1/(1/2)
x = 36
Example 15: Two men alone or three women alone can complete a piece of work in 4 days. In how many days can 1 women and one man together complete the same piece of work ?
Solution :
2Men = 3Women
1Men = 3/2Women
1Wonen+1Men
1Women+3/2Women
So now, 5/2Wonen
m1d1 = m2d2
3×4 = 5/2x?
? = 24/5 days
Example 16: Men does half as much work as women in three –fourth of the time if together they take 18 days to complete a work. How much time shall women take to do it?
Solution :B takes x days to do the work
Therefore, Men takes (2 × 3/4x)
3x/2 days to do it
(Men + Women)’s 1 day’s work = 1/18
So, 1/x + 2/3x = 1/18 or x =30.
