Maths: Inverse Proportion
Inverse Proportion means you have two quantities changing at the
same time, but whilst one quantity increases, the other quantity
decreases.
Saying this another way, inverse proportion happens when an
increase in one quantity produces an equal and proportionate
decrease in a second quantity.
If this happens, we say the two quantities are in inverse proportion.
Let's look at a few examples using the steps outlined below.
Step 1:
Identify the quantity headings and write them down as
shown below.
Step 2:
Place the two given proportionate quantities under the
correct headings as shown.
Step 3:
Multiply the two proportionate quantities given to
work out 2nd quantity for '1' unit of the first quantity.
Step 4:
Place the worked out 2nd quantity for '1' unit of the first
quantity from Step 3 under the correct heading.
Step 5:
Place the given quantity (for which you have to work out
the 2nd quantity) under the correct heading.
Step 6:
Divide your answer from Step 3 by the given quantity
in step 5.
Step 7:
The proportionate 2nd quantity for quantity 1 is your answer.
Sounds confusing, right? Not to worry! Let's head over to the
examples and I promise it won't take you long to get the hang of it.
Completing questions on inverse proportion is really a doddle!
1
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Maths: Inverse Proportion
Q1.
Q2.
Q3.
If it takes 8 workmen 9 days to construct a garage, how long will it
take 3 workmen to complete the same job?
Step 1:
No. of workmen
No. of days taken
Step 2:
8 men
=
[9 days]
Step 3:
Step 4:
1 man
1 man
=
=
[9 x 8 days]
[72 days]
Steps 5/6:
3 men
=
[ 72 days ÷ 3]
Answer:
[3 men]
=
[24 days]
6 boys building a playhouse take 12 days. How long would it take
2 boys to complete the same job?
Step 1:
No. of boys
No. of days taken
Step 2:
6 boys
=
[12days]
Step 3:
Step 4:
1 boy
1 boy
=
=
[6 x 12 days]
[72 days]
Steps 5/6:
2 boys
=
[ 72 days ÷ 2]
Answer:
[2 boys]
=
[36 days]
It takes 12 babies 2 days to consume 5 kg of baby food. How long
would it take 8 babies to consume the same amount of food?
Step 1:
No. of babies
Step 2:
12 babies
=
[2days]
Step 3:
Step 4:
1 baby
1 baby
=
=
[12 x 2 days]
[24 days]
Steps 5/6:
8 babies
=
[24 days ÷ 8]
Answer:
[8 babies]
=
[3 days]
2
No. of days taken
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Maths: Inverse Proportion
Q4.
Q5.
Q6.
Gran Ellie shares a bag of sweets between 5 of her grand children
and each child gets 3 sweets. If Gran Ellie's 3 daughters share the
same bag of sweets, how many sweets would each daughter get?
Step 1:
No. of people
No. of sweets
Step 2:
5 grand children
=
[3 sweets each]
Step 3:
Step 4:
1 grand child
1 grand child
=
=
[5 x 3 sweets]
[15 sweets]
Steps 5/6:
3 daughters
=
[15 sweets ÷ 3]
Answer:
[3 daughters]
=
[5 sweets each]
7 taxis cover a total of 210 miles in 1 hour. How long would it take
21 taxis to cover the same distance?
Step 1:
No. of taxis
No. of hours taken
Step 2:
7 taxis
=
[1 hour]
Step 3:
Step 4:
1 taxi
1 taxi
=
=
[1 x 7 hours]
[7 hours]
Steps 5/6:
21 taxis
=
[ 7 hours ÷ 21]
Answer:
[21 taxis]
=
[⅓ hour = 20 mins]
It takes 5 teachers 20 hours to mark a set of exam papers. How
long will it take 4 teachers?
Step 1:
No. of teachers
Step 2:
5 teachers
=
[20 hours]
Step 3:
Step 4:
1 teacher
1 teacher
=
=
[5 x 20 hours]
[100 hours]
Steps 5/6:
4 teachers
=
[ 100 hours ÷ 4]
Answer:
[4 teachers]
=
[25 hours]
3
No. of hours taken
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Maths: Inverse Proportion
Q7.
Q8.
Q9.
It takes 12 waiters, 6 hours to serve a 1000 meals. How long would
9 waiters take to complete the same service?
Step 1:
No. of waiters
No. of hours taken
Step 2:
12 waiters
=
[6 hours]
Step 3:
Step 4:
1 waiter
1 waiter
=
=
[12 x 6 hours]
[72 hours]
Steps 5/6:
9 waiters
=
[ 72 hours ÷ 9]
Answer:
[9 waiters]
=
[8 hours]
12 volunteers take 5 hours to help serve hot meals at a homeless
shelter. How long would it take 15 volunteers?
Step 1:
No. of volunteers
No. of hours taken
Step 2:
12 volunteers
=
[5 hours]
Step 3:
Step 4:
1 volunteers
1 volunteers
=
=
[12 x 5 hours]
[60 hours]
Steps 5/6:
15 volunteers
=
[ 60 hours ÷ 15]
Answer:
[15 volunteers]
=
[4 hours]
15 children share a box of walkers crisps and each child gets 6 bags
of crisps. How many bags would each child receive if 9 children
shared the same box of walkers crisps?
Step 1:
No. of children
Step 2:
15 children
=
[6 crisps each]
Step 3:
Step 4:
1 child
1 child
=
=
[15 x 6 crisps]
[90 crisps]
Steps 5/6:
Answer:
9 children
[9 children]
=
=
[90 crisps ÷ 9]
[10 crisps each]
4
No. of crisps
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