Word Problems using Proportion includes questions on both direct, indirect proportion. Solve the questions in our Proportion Word Problems and if you are stuck at any point you can see the step-by-step solutions provided to understand where you went wrong.
Practice the Proportions Word Problems over here to become familiar with various models asked on the concept of proportion as well as to improve your problem-solving ability. 6th Grade Math Students will find it of great value as they can get a better idea of the concept as well understand the problems quite easily.
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Solving Word Problems Using Proportions
I. Vinay runs 3km in 30 minutes. At this rate, how far could he run in 40 minutes?
Solution:
Given,
Vinay runs 3km in= 30 minutes
Let Vinay runs in 40 minutes be=x
Also, given that running 3 km in 30 min is the same as running x km in 40 minutes.
The equation of proportion can be written as
3/30=x/40
x=3/30.40
=4
Therefore, Vinay can run 4 km in 40 minutes.
II. A car travels 120 km in 3 hours. How far would it travel in 6 hours?
Solution:
Given,
A car travels in 3 hours=120 km
Let the car travel in 6 hours be x.
120/3 = x/6
x = 120/3 × 6
x =240 km
He traveled 240 km.
III. What numbers should be added to 15, 17, 34, and 38 to make the numbers proportional?
Solution:
Let the required number be k.
Then, according to the problem
15 + k, 17 + k, 34+ k and 38 + k are proportional numbers.
Therefore, 15+k/17+k = 34+k/38+k
(15 + k)(38 + k) = (17 + k)(34 + k)
570 + 15k + 38k + k2 = 578 + 17k + 34k + k2
570 + 53k = 578+51 k
53k – 51k = 578 – 570
2k = 8
k = 8/2
k = 4
Therefore, the required number is 4.
IV. Find the fourth proportional to 5,11,15?
Solution:
Let the fourth proportional to 5, 11, 15 be x
Then, 5:11::15:x
5×x=15×11
x=15×11/5
=33
∴ Fourth proportional to 4, 9, 12 is 33.
V. Find the two numbers whose mean proportion is 12 and the third proportion is 96?
Solution:
Given,
mean proportion is=12
Third Proportion=96
Let the required numbers be a and b.
\(\sqrt{ ab }\)=12 [Since, 12 is the mean proportional of a, b]
and b2/a = 96 [Since, the third proportional of a, b is 96]
Now, \(\sqrt{ ab }\) = 16
ab = 122
ab = 144
Again, b2/a = 96
b2 = 96a
a = b2/96
Substituting a = b2/96 in ab = 144
b2/96 × b = 144
b3/96 = 144
b3 = 144 × 96
b3 = 13824
b = 24
So, from equation a = b2/96we get
a = 242/96
a = 576/96
a = 6
Therefore, the required numbers are 6 and 24.
VI. What number should be added to each of 1,3,4 and 9 so that the resulting numbers make a proportion?
Solution:
Given,
1,3,4,9 are in proportion.
1/3:: 4/9
Let x be added to each of the numbers to make a proportion.
1+x/3+x:: 4+x/9+x
(1+x). (9+x)=(4+x). (3+x)
9+x+9x+x2=12+4x+3x+x2
9+10x=12+7x
3x=3
x=1
Hence 1 should be added to each 1,3,4,9.
VII. Find the fourth proportion of 8,10, and12?
Solution:
Given,
8,10,12 are in proportion.
Let x be the fourth proportion.
8/10=12/x (since they are in proportion)
8x=120
x=120/8
=15
Hence the fourth proportion is 15.
VIII. Calculate the mean proportion of 4 and 64?
Solution:
Let the mean proportion of 4 and 64 be x.
By applying the formula b2=ac
Hence x2=4.64
=256
x =16
Hence the mean proportion of 4 and 64 is 16.
Ix. In an excursion, a group of boys and girls are formed. Each group consists of 3 boys and 5 girls. How many boys are required, if 100 girls are available for such grouping?
Solution:
Given,
Each group consists of 3 boys and 5 girls.
Let the required boys be x.
3/5=x/100
x=3/5 × 100
=60
Therefore, no. of boys required are 60.
X. Jay bought 5 apples for Rs 100. How many apples he could buy for Rs 300?
Solution:
Given,
Jay bought 5 apples for =Rs 100
Let x apples are bought for Rs 300.
5/100=x/300
x=15
Therefore, 15 apples are bought for Rs 300.
XI. It takes 8 hours for 3 men to repair a road. How long will it take 8 men to do the job if they work at the same rate?
Solution:
Given,
3 men requires=8 hours
Let 8 men require x hours.
3 × 8 = 8x
x = 24/8 = 3
Hence, no. of hours required is 3.