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 ?
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,
= 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.]
= 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 ?
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,
= 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.]
= 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 ?
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,
= 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.]
= 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 ?
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,
= 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.]
= 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 ?
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.]
= 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.]
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