CBSE Class 8 Mathematics Ratio and Proportion MCQs Set 49

Multiple Choice Questions (MCQs) for Class 8 Mathematics: Ratio and Proportion

Explore reliable objective questions for Ratio and Proportion tailored for Class 8 learners. Utilizing these Mathematics multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Practice Ratio and Proportion MCQs for Class 8 Mathematics

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Multiple Choice Questions

Question 1: The contents of two vessels containing water and milk in the ratios \( 2:5 \) and \( 4:7 \) are mixed in the ratio \( 1:3 \). The ratio of water to milk in the mixture is
(a) \( 6:12 \)
(b) \( 2:5 \)
(c) \( 53:101 \)
(d) \( 4:7 \)
Show Answer & Explanation

Answer: (c) \( 53:101 \)

Explanation:
1. Water: \( \frac27+3\times\frac4{11}=\frac{106}{77} \). Milk: \( \frac57+3\times\frac7{11}=\frac{202}{77} \).
2. Ratio \( =106:202=53:101 \).

Teacher's Note:
1. Same method with fractions.

Question 2: The sum of three numbers A, B and C is \( 98 \). If \( A:B=2:3 \) and \( B:C=5:8 \), the value of \( B\div6 \) is
(a) \( 3 \)
(b) \( 6 \)
(c) \( 5 \)
(d) \( 4 \)
Show Answer & Explanation

Answer: (c) \( 5 \)

Explanation:
1. \( A:B:C=10:15:24 \), total \( 49 \) parts, so one part \( =2 \).
2. \( B=30 \) and \( 30\div6=5 \).

Teacher's Note:
1. Make the common term equal in both ratios.

Question 3: The value of \( x \) in the proportion \( 75:3=x:9 \) is
(a) \( 25 \)
(b) \( 75 \)
(c) \( 27 \)
(d) \( 225 \)
Show Answer & Explanation

Answer: (d) \( 225 \)

Explanation:
1. \( 3x=75\times9=675 \), so \( x=225 \).

Teacher's Note:
1. Cross-multiply.

Question 4: Which of the following statements are true?
(i) The compound ratio of \( 1:2 \), \( 3:5 \) and \( 5:9 \) is \( \frac16 \).
(ii) The duplicate ratio of \( 14:17 \) is \( 196:289 \).
(iii) The triplicate ratio of \( 3:5 \) is \( 27:125 \).
(iv) The fourth proportional to \( 6, 8, 9 \) is \( 42 \).
(a) (i), (ii) and (iv)
(b) (i), (ii) and (iii)
(c) (ii), (iii) and (iv)
(d) (i) and (iv)
Show Answer & Explanation

Answer: (b) (i), (ii) and (iii)

Explanation:
1. (i) \( \frac{15}{90}=\frac16 \): true.
2. (ii) and (iii) are true by definition.
3. (iv) \( \frac{8\times9}{6}=12 \), not \( 42 \): false.

Teacher's Note:
1. Check each statement separately.

Question 5: If \( 30 \) men can do a piece of work in \( 27 \) days, in how many days can \( 18 \) men do another piece of work \( 3 \) times as great?
(a) \( 135 \) days
(b) \( 45 \) days
(c) \( 90 \) days
(d) \( 81 \) days
Show Answer & Explanation

Answer: (a) \( 135 \) days

Explanation:
1. Work done is proportional to men \( \times \) days. For \( 30 \) men: \( 30\times27=810 \) units for 1 piece.
2. For \( 3 \) pieces we need \( 2430 \) units; with \( 18 \) men, days \( =\frac{2430}{18}=135 \).

Teacher's Note:
1. More work needs more man-days; fewer men need more days.

Question 6: In what ratio must a grocer mix two types of tea costing Rs. \( 35 \) and Rs. \( 28 \) per kg to get a mixture worth Rs. \( 33 \) per kg? (dearer : cheaper)
(a) \( 1:3 \)
(b) \( 2:3 \)
(c) \( 1:2 \)
(d) \( 5:2 \)
Show Answer & Explanation

Answer: (d) \( 5:2 \)

Explanation:
1. By alligation: dearer : cheaper \( =(33-28):(35-33)=5:2 \).

Teacher's Note:
1. Use the cross rule of alligation.

Question 7: The sum of two numbers is \( 40 \) and their difference is \( 4 \). The ratio of the greater to the smaller is
(a) \( 10:11 \)
(b) \( 11:9 \)
(c) \( 11:10 \)
(d) \( 9:11 \)
Show Answer & Explanation

Answer: (b) \( 11:9 \)

Explanation:
1. Numbers: \( \frac{40+4}{2}=22 \) and \( \frac{40-4}{2}=18 \).
2. Ratio \( =22:18=11:9 \).

Teacher's Note:
1. Greater \( =\frac{\text{sum}+\text{difference}}{2} \).

Question 8: If \( 5 \) men or \( 7 \) women can earn Rs. \( 875 \) per day, how much would \( 10 \) men and \( 5 \) women earn per day?
(a) Rs. \( 2375 \)
(b) Rs. \( 2735 \)
(c) Rs. \( 2300 \)
(d) Rs. \( 2400 \)
Show Answer & Explanation

Answer: (a) Rs. \( 2375 \)

Explanation:
1. One man earns \( \frac{875}{5}=175 \) and one woman \( \frac{875}{7}=125 \).
2. \( 10\times175+5\times125=1750+625=2375 \).

Teacher's Note:
1. Find the daily wage of each person.

Question 9: A bag contains equal numbers of one-rupee, \( 50 \)-paise and \( 25 \)-paise coins. If the total value is Rs. \( 35 \), the number of coins of each type is
(a) \( 20 \)
(b) \( 100 \)
(c) \( 25 \)
(d) \( 40 \)
Show Answer & Explanation

Answer: (a) \( 20 \)

Explanation:
1. Value of one set \( =1+0.5+0.25=1.75 \).
2. Number \( =\frac{35}{1.75}=20 \).

Teacher's Note:
1. Find the value of one coin of each type together.

Question 10: If \( x:y=5:2 \), then \( (8x+9y):(8x+2y) \) is equal to
(a) \( 29:22 \)
(b) \( 8:11 \)
(c) \( 22:29 \)
(d) \( 2:1 \)
Show Answer & Explanation

Answer: (a) \( 29:22 \)

Explanation:
1. Take \( x=5,\ y=2 \): \( 8x+9y=40+18=58 \) and \( 8x+2y=40+4=44 \).
2. \( 58:44=29:22 \).

Teacher's Note:
1. Substitute values in the given ratio.

Question 11: Which of the following statements are true?
(i) In \( 5:15=2:x \), \( x=6 \).
(ii) The fourth proportional to \( 1, 2, 3 \) is \( 6 \).
(iii) The fourth proportional to \( 2.5, 1.5, 1.5 \) is \( 0.9 \).
(iv) The third proportional to \( 5 \) and \( 10 \) is \( 25 \).
(a) (i), (ii) and (iv)
(b) (i) and (iv)
(c) (ii), (iii) and (iv)
(d) (i), (ii) and (iii)
Show Answer & Explanation

Answer: (d) (i), (ii) and (iii)

Explanation:
1. (i) \( x=\frac{15\times2}{5}=6 \): true.
2. (ii) \( \frac{2\times3}{1}=6 \): true.
3. (iii) \( \frac{1.5\times1.5}{2.5}=0.9 \): true.
4. (iv) third proportional \( =\frac{10^2}{5}=20 \), not \( 25 \): false.

Teacher's Note:
1. Third proportional to \( a, b \) is \( \frac{b^2}{a} \).

Question 12: The value of \( x \) in the proportion \( 15:5=x:2 \) is
(a) \( 16 \)
(b) \( 12 \)
(c) \( 6 \)
(d) \( 15 \)
Show Answer & Explanation

Answer: (c) \( 6 \)

Explanation:
1. \( 5x=15\times2 \), so \( x=6 \).

Teacher's Note:
1. Product of extremes equals product of means.

Question 13: The fourth proportional to \( 6, 8 \) and \( 9 \) divided by \( 4 \) gives
(a) \( 12 \)
(b) \( 4 \)
(c) \( 2 \)
(d) \( 3 \)
Show Answer & Explanation

Answer: (d) \( 3 \)

Explanation:
1. Fourth proportional \( =\frac{8\times9}{6}=12 \).
2. \( 12\div4=3 \).

Teacher's Note:
1. Find the fourth proportional first.

Question 14: A work force of \( 420 \) men can finish a piece of work in \( 9 \) months. How many men are needed to finish it in \( 7 \) months?
(a) \( 210 \)
(b) \( 540 \)
(c) \( 240 \)
(d) \( 175 \)
Show Answer & Explanation

Answer: (b) \( 540 \)

Explanation:
1. Men \( \times \) months is constant: \( 420\times9=3780 \).
2. \( \frac{3780}{7}=540 \).

Teacher's Note:
1. Less time needs more men.

Question 15: If \( a:b=8:9 \), \( b:c=9:10 \) and \( c:d=10:11 \), then \( a:d \) is
(a) \( 2:1 \)
(b) \( 11:8 \)
(c) \( 8:11 \)
(d) \( 29:22 \)
Show Answer & Explanation

Answer: (c) \( 8:11 \)

Explanation:
1. \( a:d=\frac89\times\frac9{10}\times\frac{10}{11}=\frac8{11} \).

Teacher's Note:
1. Chain the ratios by multiplication.

Question 16: The number which, when added to each term of the ratio \( 11:23 \), makes it equal to \( 4:7 \) is
(a) \( 10 \)
(b) \( 5 \)
(c) \( 15 \)
(d) \( 20 \)
Show Answer & Explanation

Answer: (b) \( 5 \)

Explanation:
1. \( \frac{11+x}{23+x}=\frac47 \), so \( 77+7x=92+4x \).
2. \( 3x=15 \), \( x=5 \).

Teacher's Note:
1. Form the equation and cross-multiply.

Question 17: The subtriplicate ratio of \( 343:729 \) is
(a) \( 7:9 \)
(b) \( 49:81 \)
(c) \( 343:243 \)
(d) \( 14:18 \)
Show Answer & Explanation

Answer: (a) \( 7:9 \)

Explanation:
1. Subtriplicate ratio means cube roots: \( 7:9 \).

Teacher's Note:
1. Sub-triplicate is the cube-root ratio.

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Multiple Choice Questions (MCQs) for Class 8 Mathematics Ratio and Proportion

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FAQs

Where can I access latest CBSE Class 8 Mathematics Ratio and Proportion MCQs Set 49?

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Are Assertion-Reasoning and Case-Study MCQs included in the Mathematics Class 8 material?

Yes, our CBSE Class 8 Mathematics Ratio and Proportion MCQs Set 49 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CBSE paper is now competency-based.

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By solving our CBSE Class 8 Mathematics Ratio and Proportion MCQs Set 49, Class 8 students can improve their accuracy and speed which is important as objective questions provide a chance to secure 100% marks in the Mathematics.

Do you provide answers and explanations for CBSE Class 8 Mathematics Ratio and Proportion MCQs Set 49?

Yes, Mathematics MCQs for Class 8 have answer key and brief explanations to help students understand logic behind the correct option as its important for 2026 competency-focused CBSE exams.

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