Trick/Theory:- If X1 men or Y1 women can complete a work in D days. 

Then, X2 men and Y2 women together can complete the same work in -

^D/_{(X2/X1 + Y2/Y1)}  or ^DX1Y1/_{(X1Y2 + X2Y1)}

or,

Let's solve some Questions....

Q-1) If 4 men or 6 women can finish a piece of work in 20 days, in how many days can 6 men and 11 women finish it ?

a) 6 days

b) 7 days

c) 8 days

d) 9 days

Solⁿ:- If 4 men (X1) or 6 women (Y1) can finish a piece of work in 20 days (D).
In how many days can 6 men (X2) and 11 women (Y2) finish it ?

Now apply 1st Maths Tricks for Time and Work Questions 

^D/_{(X2/X1 + Y2/Y1)}

Now put X1=4, Y1=6, D=20, X2=6 and Y2=11

^D/_{(X2/X1 + Y2/Y1)}

= ²⁰ / _{(6/4 + 11/6)}

= ²⁰ / ₍20/6)

= ^{20 * 6} / 20

= 6

or,

Now apply 2nd Maths Tricks for Time and Work Questions 

^DX1Y1/_{(X1Y2 + X2Y1)}

Now put X1=4, Y1=6, D=20, X2=6 and Y2=11

^DX1Y1/_{(X1Y2 + X2Y1)}

= ^{20 * 4 * 6} / (4*11 + 6*6)

= ^{20 * 4 * 6} / (44 + 36)

= ^{20 * 4 * 6} / 80

= ^{4 * 6} / 4

= 6

Your answer a) 6 days. [So, In 6 days can 6 men and 11 women finish it.]

Q-2) If 6 men or 10 women can reap a field in 86 days, how long will 10 men and 12 women take to reap it ?

a) 25 days

b) 30 days

c) 35 days

d) 40 days

Solⁿ:- If 6 men (X1) or 10 women (Y1) can reap a field in 86 days (D), 
how long will 10 men (X2) and 12 women (Y2) take to reap it ?

Now apply 1st Maths Tricks for Time and Work Questions 

^D/_{(X2/X1 + Y2/Y1)}

Now put X1=6, Y1=10, D=86, X2=10 and Y2=12

  ^D/_{(X2/X1 + Y2/Y1)}

= ⁸⁶ / (10/6 + 12/10)

= ⁸⁶ / (5/3 + 6/5)

= ⁸⁶ / (43/15)

= ^{86 * 15} / 43

= 2 * 15

= 30

or,

Now apply 2nd Maths Tricks for Time and Work Questions 

^DX1Y1/_{(X1Y2 + X2Y1)}

Now put X1=6, Y1=10, D=86, X2=10 and Y2=12

^DX1Y1/_{(X1Y2 + X2Y1)}

= ^{86 * 6 * 10} / _{(6*12 + 10*10)}

= ^{86 * 6 * 10} / (72 + 100)

= ^{86 * 6 * 10} / 172

= 3 * 10

= 30

Your answer b) 30 days. [So, In 30 days 10 men and 12 women take to reap it.]

Q-3) If 3 men or 9 boys can finish a piece of work in 21 days, in how many days can 5 men and 6 boys together do the same piece of work ?

a) 8 days

b) 12 days

c) 14 days

d) N.O.T.

Solⁿ:- If 3 men (X1) or 9 boys (Y1) can finish a piece of work in 21 days (D).
In how many days can 5 men (X2) and 6 boys (Y2) together do the same piece of work ?

Now apply 1st Maths Tricks for Time and Work Questions 

^D/_{(X2/X1 + Y2/Y1)}

Now put X1=3, Y1=9, D=21, X2=5 and Y2=6

^D/_{(X2/X1 + Y2/Y1)}

= ²¹ / (5/3 + 6/9)

= ²¹ / (5/3 + 2/3)

= ²¹ / 7/3

= ^{21 * 3} / 7

= 3 * 3

= 9

or,

Now apply 2nd Maths Tricks for Time and Work Questions 

^DX1Y1/_{(X1Y2 + X2Y1)}

Now put X1=3, Y1=9, D=21, X2=5 and Y2=6

^DX1Y1/_{(X1Y2 + X2Y1)}

= ^{21 * 3 * 9} / (3*6 + 5*9)

= ^{21 * 3 * 9} / (18 + 45)

= ^{21 * 27} / 63

= 9

Your answer d) N.O.T days. [So, In 9 days can 5 men and 6 boys together do the same piece of work.]

Q-4) If 2 men or 4 women can finish a piece of work in 44 days, in how many days can 3 men and 5 women finish it ?

a) 8 days

b) 12 days

c) 15 days

d) 16 days

Solⁿ:- If 2 men (X1) or 4 women (Y1) can finish a piece of work in 44 days (D).
In how many days can 3 men (X2) and 5 women (Y2) finish it ?

Now apply 1st Maths Tricks for Time and Work Questions 

^D/_{(X2/X1 + Y2/Y1)}

Now put X1=2, Y1=4, D=44, X2=3 and Y2=5

^D/_{(X2/X1 + Y2/Y1)}

= ⁴⁴ / _{(3/2 + 5/4)}

= ⁴⁴ / _11/4

= ^{44 * 4} / ₁₁

= 4 * 4

= 16

or,

Now apply 2nd Maths Tricks for Time and Work Questions 

^DX1Y1/_{(X1Y2 + X2Y1)}

Now put X1=2, Y1=4, D=44, X2=3 and Y2=5

^DX1Y1/_{(X1Y2 + X2Y1)}

 = ^{44 * 2 * 4} / _{(2*5 + 3*4)}

= ^{44 * 8} / _{(10 + 12)}

= ^{44 * 8} / ₂₂

= 2 * 8

= 16

Your answer d) 16 days. [So, In 16 days can 3 men and 5 women finish it.]

Q-5) If 10 men or 18 boys complete a work in 15 days. Then, in how many days, 25 men and 15 boys will complete the work ?

a) ⁹ / 2 days

b) 9 days

c) 18 days

d) 36 days

Solⁿ:- If 10 men (X1) or 18 boys (Y1) complete a work in 15 days (D).
In how many days, 25 men (X2) and 15 boys (Y2) will complete the work ?

Now apply 1st Maths Tricks for Time and Work Questions 

^D/_{(X2/X1 + Y2/Y1)}

Now put X1=10, Y1=18, D=15, X2=25 and Y2=15

^D/_{(X2/X1 + Y2/Y1)}

= ¹⁵ / _{(25/10 + 15/18})

= ¹⁵ / _{(5/2 + 5/6})

= ¹⁵ / 20/6

= ^{15 * 6} / 20

= ^{3 * 6} / 4

= ^{3 * 3} / 2

= ⁹ / 2

or,

Now apply 2nd Maths Tricks for Time and Work Questions 

^DX1Y1/_{(X1Y2 + X2Y1)}

Now put X1=10, Y1=18, D=15, X2=25 and Y2=15

^DX1Y1/_{(X1Y2 + X2Y1)}

= ^{15 * 10 * 18} / (10*15 + 25*18)

= ^{15 * 10 * 18} / (150 + 450)

= ^{15 * 10 * 18} / 600

= ¹⁸ / 4

= ⁹ / 2

Your answer a) ⁹ / 2 days. [So, In 9/2 days 25 men and 15 boys will complete the work.]

Time and Work Trick

💢Time and Work Aptitude Tricks, this time and work aptitude  tricks can help you to find answer of Time and Work problems in only few seconds. This short tricks for time and work can help you any competitive exam like SSC CGL, SSC CHSL, SSC CPO, BANK, RAILWAY, UPSC etc.

Que.01) If 10(A) men or 20 (B) women or 40(C) boys can do a piece of work in 7 days.
Then 5 (A1) men, 5 (B1) women and 5(C1) boys together can complete the same work
in how many days (D1)?
a) 5 days
b) 4 days
c) 6 days
d) 8 days
Trick:      D/(A1/A + B1/B + C1/C)
               =7/(5/10 + 5/20 + 5/40)
               =7/(1/2 + 1/4 + 2/8)
               =7/{(4+2+1)/8}
               =7/(7/8)
               =(7*8)/7 = 8 days (Ans.)

Que.02) If 1 man or 2 women or 3 boys can do a work in 88 days.
 1 man, 1 woman and 1 boys together will complete the same work
in how many days?
a) 36 days
b) 42 days
c) 48 days
d) 54 days

Trick:      D/(A1/A + B1/B + C1/C)
               =88/(1/1 + 1/2 + 1/3)
               =88/{(6+3+2)/6}
               =88/(11/6)
               =(88*6)/11 = 48 days (Ans.)

Que.03) 3 men or 5 women or 8 boys can finish a work in 38 days.
Then in how many days 6 men and 10 women and 6 boys will complete
this work?
A) 8
B) 12
C) 9
D) None of these.

Trick:      D/(A1/A + B1/B + C1/C)
               =38/(6/3 + 10/5+ 6/8)
               =38/(2+2+3/4)
               =38/{(8+8+3)/4}
               =38/(19/4)
               =(38*4)/19= 8 days (Ans.)

Que.4) If 2 men or 6 women or 4 boys can finish a work in 99 days.
How many days will one man, one woman and one boy together take
to finish the same work?
A) 44 days
B) 54 days
C) 64 days
D) 104 days
E) None of these.

Trick:      D/(A1/A + B1/B + C1/C)
               =99/(1/2+ 1/6+ 1/4)
               =99/{(6+2+3)/12}
               =99/(11/12)
               =(99*12)/11 = 108
               So, Answer is (E) none of these.

Que.05) If 40 men or 60 women or 80 children can do a piece of work in 6 month.
Then 10 men, 10 women and 10 children together do half of the work in how many days?
A) 5 * 6/13 months
B) 6 months
C) 5 * 7/13 months
D) 11 * 1/13 months

Trick:      D/(A1/A + B1/B + C1/C)
               =6/(10/40 + 10/60 + 10/80)
               =6/(1/4 + 1/6 + 1/8)
               =6/{(6+4+3)/24}
               =6/(13/24)
               =(6*24)/13 = 11(1/13) (Ans.)