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Byju's Answer
Standard VIII
Mathematics
Compound Proportion
40 workers wo...
Question
40 workers working for 8 hours per day digs a hole of 1088
m
3
. If 45 workers work for 6 hours a day, then what volume of the hole they can dig in
m
3
?
918
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Solution
The correct option is
A
918
Here, the number of workers is directly proportional to the number of hours per day and volume of hole.
Number of workers
Number of hours a day
Volume of hole
40
8
1088
m
3
45
6
x
40:45 = 8:9
8:6 = 4:3
1088:
x
Number of workers
∝
Volume of the hole
⇒
8
:
9
=
1088
:
x
.
.
.
(
i
)
Number of hours a day
∝
Volume of the hole
⇒
4
:
3
=
1088
:
x
.
.
.
(
i
i
)
From (i) and (ii), we get,
1088 :
x
=
compound ratio of
8
:
9
and
4
:
3
⇒
1088
:
x
=
(
8
:
9
)
×
(
4
:
3
)
⇒
1088
:
x
=
(
8
×
4
)
:
(
9
×
3
)
⇒
1088
:
x
=
(
32
:
27
)
∵
Product of means = Product of extremes
⇒
x
×
32
=
1088
×
27
⇒
x
=
918
m
3
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