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R<br />
13 Veto<br />
follow us: facebook.com/vetotrivandrum 14<br />
Work and Time<br />
type - i<br />
1. A can do a work in 6 days B can<br />
do the some work in 3 days. In<br />
howmany days working together<br />
they will finish the same work?<br />
(a) 3 days (b) 9 days<br />
(c) 2 days (d) None<br />
Ans: (c) 2 days<br />
A can do a work in x days<br />
B can do the same work in y days<br />
then A and B can do the work in<br />
xy<br />
x+<br />
y<br />
OR<br />
days<br />
A→ x days<br />
B→ y days<br />
A+B =<br />
Exp: x = 6<br />
y = 3<br />
6× 3 6×<br />
3<br />
= = 2days<br />
6+<br />
3 9<br />
2. A and B can seperately finish a<br />
work in 10 days and 15 days<br />
respectively. In how may days<br />
working together, they will finish<br />
the work?<br />
(a) 6 days<br />
(c) 9 days<br />
xy<br />
x+<br />
y<br />
Ans: (a) 6 days<br />
(b) 2 days<br />
(d) 3 days<br />
Exp: x = 10, y = 15<br />
xy 10× 15 10×<br />
15<br />
= = = 6 days<br />
x+ y 10 + 15 25<br />
type - iI<br />
3. A can do a work in 30 days.<br />
B can do the same work in 60<br />
days. C can do the same work<br />
in 80 days. A, B and C working<br />
together, in how many days they<br />
will finish the same work?<br />
(a) 9 days (b) 16 days<br />
(c) 10 days (d) None of these<br />
Ans: (b) 16 days<br />
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A→ x days<br />
B → y days<br />
C → z days<br />
ü<br />
A+B+C =<br />
days<br />
xy + yz + xz<br />
Exp: x = 30, y = 60, z = 80<br />
xyz<br />
xy + yz + xz<br />
30× 60×<br />
80<br />
=<br />
30× 60 + 60× 80 + 30×<br />
80<br />
30× 60×<br />
80<br />
=<br />
1800 + 4800 + 2400<br />
30× 60×<br />
80<br />
= = 16 days<br />
9000<br />
4. A, B and C can do a work seperately<br />
in 10 days, 15 ays and 30<br />
days. In how many days working<br />
together they will finish the work?<br />
(a) 6 days<br />
(c) 4 days<br />
Ans: (b) 5 days<br />
(b) 5 days<br />
(d) 2 days<br />
Exp: x = 10, y = 15, z = 30<br />
xyz<br />
=<br />
xy + yz + xz<br />
10× 15×<br />
30<br />
=<br />
10× 15 + 15× 30 + 10×<br />
30<br />
10× 15×<br />
30<br />
=<br />
150 + 450 + 300<br />
10× 15×<br />
30<br />
= = 5 days<br />
900<br />
type - iII<br />
5. A and B together can complete a<br />
work in 12 days. If A alone can<br />
finish the same work in 18 days.<br />
In how many days B alone can<br />
finish the same work?<br />
(a) 18 days (b) 36 days<br />
(c) 72 days (d) None of these<br />
Ans: (b) 36 days<br />
A+B→ x days<br />
A → y days<br />
B→<br />
xy<br />
y−<br />
x<br />
days<br />
Exp: x = 12, y = 18<br />
xy<br />
y x<br />
12× 18 12×<br />
18<br />
= = = 36 days<br />
18 12 6<br />
6. A and B and C together can complete<br />
a work in 10 days. If B and<br />
C together alone can complete the<br />
same work in 15 days. In how<br />
many days A alone can complete<br />
the same work?<br />
(a) 15 days<br />
(c) 25 days<br />
Ans: (b) 30 days<br />
(b) 30 days<br />
(d) None of these<br />
Exp: x = 10, y = 15<br />
xy<br />
y x<br />
10× 15 10×<br />
15<br />
= = = 30 days<br />
15 10 5<br />
type - iV<br />
7. If 12 men can do a job in 16 days.<br />
In how many days 8 men can<br />
complete the work?<br />
(a) 12 days (b) 24 days<br />
(c) 30 days (d) None of these<br />
Ans: (b) 24 days<br />
12m<br />
→16days<br />
Exp :<br />
8 m → ?<br />
12×<br />
16<br />
= = 24 days<br />
8<br />
Short Cut<br />
Numerator = Multiply the 1 st row<br />
Denominator = 2 nd row<br />
8. 21 men can do a job in 10 days.<br />
In how many men can do finish<br />
the same work in 7 days?<br />
(a) 20 (b) 30<br />
(c) 15 (d) None of these<br />
Ans: (b) 30<br />
21m<br />
→10days<br />
Exp :<br />
? → 7days<br />
21×<br />
10<br />
= = 30 men<br />
7<br />
9. In a camp, there are 50 days food<br />
in 20 peoples. If 5 more peoples<br />
attend the camp. In how many<br />
days food are sufficient in the<br />
camp?<br />
(a) 30 days<br />
(c) 40 days<br />
Ans: (b) 30<br />
(b) 25 days<br />
(d) None of these<br />
5 more people attend the camp<br />
∴Total people = 20 + 5 = 25<br />
20 → 50days<br />
ü →<br />
20×<br />
50<br />
Exp : = 40 days<br />
25<br />
type - V<br />
10. 6 men or 8 women can do a job<br />
in 46 days. How long will 8 men<br />
and 20 women do the same job?<br />
(a) 10 days (b) 12 days<br />
(c) 6 days (d) None of these<br />
Ans: (b) 12 days<br />
6m or 8w → 46 days<br />
8m and 20 w → ?<br />
No. of days (or/and)<br />
6× 8× 46 6× 8×<br />
46<br />
= =<br />
6× 20 + 8× 8 120 + 64<br />
6× 8×<br />
46<br />
= = 12 days<br />
184<br />
Short-cut<br />
Multiply the 1st row (Numerator)<br />
Cross xied and added each other<br />
(denominator)<br />
11. 3 men or 4 women can do a job<br />
in 43 days. How long will 7 men<br />
and 5 women do the same job?<br />
(a) 12 days (b) 24 days<br />
(c) 48 days (d) 6 days<br />
Ans: (a) 12 days<br />
3m or 4w → 43 days<br />
=<br />
7m and 5 w → ?<br />
3× 4× 43 3× 4×<br />
43<br />
Exp : = = = 12 days<br />
15 + 28 43<br />
12. 8 men or 12 women can do a job<br />
in 18 days. How long will 18 men<br />
and 9 women do the same job?<br />
(a) 3 days (b) 6 days<br />
(c) 12 days (d) None of these<br />
Ans: (b) 6 days<br />
8m or 12w →18<br />
days<br />
18m and 9 w → ?<br />
8× 12× 18 8× 12×<br />
18<br />
Exp : ℵ<br />
72 + 216 288<br />
type - VI<br />
6days<br />
13. 1 men or 2 women or 3 boys<br />
do a piece of job in 44 days. In<br />
howmany days to finish the same<br />
piece of job done by 1 men and<br />
1 women and 1 boy?<br />
(a) 44 days (b) 24 days<br />
(c) 22 days (d) 12 days<br />
Ans: (b) 24 days<br />
1M or 2W or 3B → 44days<br />
Exp :<br />
1M and 1W and 1B → ?