Worksheet on Word Problems on Ratios

On this page, you will find Worksheets on Ratio Word Problems that are meant for 6th Grade Math Students. Free Printable Worksheet on Word Problems on Ratio has questions for what is meant by ratio, how to simplify ratios, etc. The benefit of practicing from the Ratio Word Problems Worksheet is that Students will get to apply their knowledge of ratios and interpret ratios in real-life scenarios.

Students can use the interactive and easy-to-understand manner designed Worksheet on Ratio Word Problems and master the topic of ratios. Knowledge of Ratios is a must-have skill to get grip on arithmetic as well as to enable thinking skills and our Ratio Word Problems Worksheet with Answers PDF does that pretty well.

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Ratio Problems with Solutions PDF

I. A flower vase has 42 Roses of which 12 are white and the remaining are Red roses. What is the ratio of white to
Red Roses?

Solution:

Given,
No. of Roses=42
No. of white Roses=12
No. of Red Roses=42-12=30
The ratio of white Roses to Red Roses=12/30
=4/10=2/5
Hence, the ratio of White roses to Red roses is 2/5.


II. Rs 8000 are to be divided between Ajay and Vijay in the ratio 4: 6. How much does each get?

Solution:

Given,
Money divided between Ajay and Vijay=Rs 8000
The amount is divided in the ratio=4:6
Ajay gets the amount=4x
Vijay gets the amount=6x
So 4x+6x=Rs 8000
10x=Rs 8000
x=Rs 8000/10
=800
Ajay gets the amount=4(800)=3200
Vijay gets the amount=6x=6(800)=4800
Therefore, Ajay gets Rs 3200, Vijay gets Rs 4800.


III. In an office, there are 700 men and 300 women. What is the ratio of women to all staff?

Solution:

Given,
No. of men in the office=700
No. of women in the office=300
No. of staff in the office=700 + 300=1000
The ratio of women to all the staff=300/1000
=3:10


IV. The weight of the Ananya is equal to the sum of the weights of Sandhya and Sindhu. The ratio of the weights of the Sandhya to that of the Sindhu is 3:4. If the weight of Ananya is 63. Find the weights of his Sandhya and Sindhu?

Solution:

Given,
The weight of Ananya is =63
The ratio of the weights of the Sandhya to that of the Sindhu is= 3:4
Let the common factor be x.
3x+4x=63
7x=63
x=63/7=9
The weight of Sandhya is =3x=3(9)=27
The weight of Sindhu is=4x=4(9)=36
Hence the weights of Sandhya and Sindhu are 27,36.


V. The money of Rs 48,000 is invested by the three friends Jay, Vijay, and Ajay in the ratio 2: 6: 8. How much does each friend invest?

Solution:

Given,
The money invested by three friends=Rs 48,000
Money is invested in the ratio=2:6:8
Let the common factor be x.
2x+6x+8x=Rs 48,000
16x=Rs 48,000
x=48000/16
=Rs 3000
The money invested by Jay=2x=2(3000)=Rs 6000
The money invested by Vijay=6x=6(3000)=Rs 18000
The money invested by Ajay=8x=8(3000)=Rs 24000
Hence, the money invested by Jay, Vijay, and Ajay are Rs 6000, Rs 18000, Rs 24000.


VI. In a bag of white and red dresses, the ratio of white dresses to red dresses is 4:5. If the bag contains 12 white sweets, how many red dresses are there?

Solution:

Given,
The ratio of white dresses to red dresses is =4:5
No. of white dresses in the bag=12
Let x be the number of red dresses.
Dresses are in the ratio=4/5=12/x
4x=12.5
4x=60
x=60/4=15
Therefore, there are 15 red dresses.


VII. In a shop, there are rice, wheat, and corn in the ratio 3:4:5. If the shopkeeper sold 6 kg of rice, how much corn does he sold?

Solution:

Let x be the amount of corn sold.
rice/corn=3/5
The shopkeeper sold 6 kg of rice, corn sell by the shopkeeper= 6/x
Since they are in proportion,
3/5=6/x
3x=5 .6
3x=30
x=30/3=10
Therefore, Corn sell by the shopkeeper is 10 kg.


VIII. The Selling Price of the Rice is increased from Rs.1000 to Rs.1200 this month. Find the ratio of the increased price to the original price?

Solution:

Given,
The original price of the rice=Rs 1000
The increased selling price of the rice=Rs 1200
The ratio of increased Price to Original Price=1200/1000
=6/5
Hence, the ratio of the increased price of rice to the original price is 6/5.


IX. The average salary of three friends Vinay, Vignesh, and Vijay is Rs 60,000 and their salaries are in the proportion 2 : 4: 6. Find the salaries of each of them?
ii) Also find the highest salaried man?

Solution:

Given,
The average salary of three friends is= Rs 60,000
From the ratio 2 : 4 : 6, the Salaries of three friends are 2x, 4x and 6x.
(2x + 4x + 6x) / 3 = 60,000
12x = 1,80,000
x = 15000
Salary of the Vinay = 2x = 2(15000) = 30,000
Salary of the Vignesh= 4x = 4(15000) = 60,000
salary of the Vijay= 6x = 6(15000) = 90,000
Hence, the highest salaried person is Vijay.


X. The ratio of the prices of two items was 13: 24. Two years later when the price of the first has increased by 20% and that of the second by Rs 500, the ratio of the prices becomes 15: 28. Find the original price of the first house?

Solution:

From the given ratio of 13: 24,
Original price of the 1st item = 13x
Original price of the 2nd item = 24x
After increment in prices,
Price of the 1st item = 13x + 20% of 13x
= 13x + 2.6x
= 15.6x
Price of the 2nd item = 24x + 500
After an increment in prices, the ratio of prices becomes 15:28.
Then, we have
15.6x : (24x + 500) = 15 : 28
Use cross-product rule.
28(15.6x) = 15(24x + 500)
436.8 x = 360 x + 7500
76.8x = 7500
x = 97.65
Then, the original price of the first item is
= 13x
= 13(97.65)= 1269.45
Hence, the original price of the first house is Rs 1269.45.


XI. In Jaya’s class, 24 of the students are tall and 10 are short. In Maya’s class, 30 students are tall and 16 students are short. Which class has a higher ratio of tall to short students?

Solution:

Given,
In Jaya’s class, No. of tall students=24
No. of short students=10
The ratio of tall to short students is=24/10=12/5=2.4
In Maya’s class, No. of tall students=30
No. of short students=16
The ratio of tall to short students=30/16
=15/8=1.875
Therefore, Jaya’s class has a higher ratio of tall to short students.


XII. The ratio of the no. of boys to the no. of girls in a school of 550 students is 3: 4. If 15 new girls are admitted to the school, find how many new boys may be admitted so that the ratio of the no. of boys to the no. of girls may change to 3: 2?

Solution:

Given ratio is 3:4
The sum of the terms in the given ratio is
= 3 + 4= 7
So, no. of boys in the school is
= 550 ⋅ (3/7)= 235
No. of girls in the school is
= 550 ⋅ (4/7)= 314
The number of new girls admitted to the school is 15.
Let x be the no. of new boys admitted to the school.
After the above new admissions,
No. of boys in the school = 235 + x
No. of girls in the school = 314 + 15 = 329
Given, The ratio after the new admission is 2 : 3.
Then, we have
(235 + x) : 329 = 3: 2
Use cross-product rule.
2(235 + x) = 329 ⋅ 3
470 + 2x = 987
2x = 517
x =258
So, the number of new boys admitted to the school is 258.


XIII. The ratio of red marbles to blue marbles in a bag is 4:5. If there are 54 marbles in the bag, how many of the marbles are red?

Solution:

Given,
The ratio of red marbles to blue marbles in a bag is 4:5
Let the red marbles be 4x.
Let the blue marbles be 5x.
No. of marbles in the bag=54
4x+5x=54
9x=54
x=54/9=6
No. of red marbles = 4x=4(6)=24
Hence, No.of red marbles = 24.


 

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