All Free Mathematics MCQs with Answers

• A. 30, 19
• B. 21, 37
• C. 15, 34
• D. 15, 27Enrolling In Online Certification Courses

Explanation: Let the numbers be 5k and 9k. After decreasing each by 5, (5k − 5):(9k − 5) = 5:11, so 11(5k − 5) = 5(9k − 5), giving k = 3 and numbers 15…

• A. 8.96
• B. 8
• C. 4.5
• D. 6.2

Explanation: If c is the third proportional to 3.5 and 5.6, then 3.5:5.6 = 5.6:c, so c = 5.6² ÷ 3.5 = 31.36 ÷ 3.5 = 8.96.

• A. 360
• B. 380
• C. 375
• D. 400

Explanation: The flour-to-sugar ratio is 400 g:500 g = 4:5. For 300 g of flour, the sugar needed is 300 g × 5/4 = 375 g.

• A. 32:35
• B. 67:56
• C. 5:14
• D. 5:7

Explanation: Make the two expressions for Y equal: X:Y = 5:8 and Y:Z = 4:7, so multiply the second ratio by 2 to get Y:Z = 8:14.

• A. 3:1
• B. 4:1
• C. 3:4
• D. 4:3

Explanation: By alligation, the quantities of Rs.13 rice and Rs.19 rice are in the ratio (19 − 14.2):(14.2 − 13) = 4.8:1.2 = 4:1.

• A. Rs.100
• B. Rs.700
• C. Rs.1600
• D. Rs.2000

Explanation: A and D differ by 7 − 2 = 5 ratio parts, and this difference is Rs.500, so one part is Rs.500 ÷ 5 = Rs.100.

• A. 18
• B. 15
• C. 12
• D. 5

Explanation: Interpret the proportion as 2x:25 = 6:(x/3), giving 2x/25 = 6/(x/3) = 18/x. Hence 2x² = 450, so x² = 225 and the positive value is x = 15.

• A. 1:2
• B. 3:5
• C. 1:3
• D. 3:4

Explanation: For a ratio a:b and total 72, the sum of ratio parts must divide 72. Ratios 1:2, 3:5 and 1:3 give integer pairs, but 3:4 has 7 parts and…

• A. 2:3
• B. 3:2
• C. 3:4
• D. 4:3

Explanation: Let the car distance be x km, so the train distance is x + 150 km. Then x + x + 150 = 750, giving 2x = 600 and x = 300 km; train distance…

• A. 8
• B. 6
• C. 12
• D. 18

Explanation: Let the numbers be 3k, 5k and 6k. Their squared sum is (3k)² + (5k)² + (6k)² = 9k² + 25k² + 36k² = 70k², so 70k² = 280 and k² = 4, giving…

• A. 9:19
• B. 19:9
• C. 15:28
• D. 28:15

Explanation: With equal total costs, 4500 rupees per square foot × flat area = 9500 rupees per square foot × commercial area.

• A. 44
• B. 55
• C. 66
• D. 77

Explanation: Make the second term common: 8:11 becomes 40:55, while 5:7 becomes 55:77.

• A. Rs.18000
• B. Rs.13000
• C. Rs.15000
• D. Rs.10000

Explanation: Let one singer's share be s. From 3 dancers = 2 singers, one dancer gets 2s/3, and from 3 comperes = 2 dancers, one compere gets 4s/9…

• A. 4
• B. 6
• C. 3
• D. 2

Explanation: Write the numbers as 2k and 3k. Their cubes give (2k)^3 + (3k)^3 = 8k^3 + 27k^3 = 35k^3 = 280, so k^3 = 8 and k = 2; the smaller number is…

• A. 38
• B. 35
• C. 10
• D. 28

Explanation: Direct variation means x = k(4y - 1). Using x = 14 when y = 2 gives 14 = k(8 - 1) = 7k, so k = 2; when y = 5, x = 2(20 - 1) = 38.

• A. 6:10
• B. 13:20
• C. 3:4
• D. 35:33

Explanation: Take the original numbers as 5k and 8k. After the increases they become 5k(1.30) = 6.5k and 8k(1.25) = 10k, so their ratio is 6.5:10 =…

• A. 2:5
• B. 4:5
• C. 6:5
• D. 8:5

Explanation: Let A = 2k and B = 3k from A:B = 2:3. Since B:C = 3:4, C = 4k; and A:D = 4:5 gives D = (5/4)(2k) = 5k/2. Therefore C:D = 4k:5k/2 = 8:5.

• A. 63
• B. 31
• C. 21
• D. 27

Explanation: The fourth proportion x satisfies 3:7 = 9:x. Cross-multiplication gives 3x = 7 x 9 = 63, so x = 21.

• A. 2 : 5
• B. 3 : 7
• C. 5 : 3
• D. 7 : 3

Explanation: Let the first and second numbers be A and B. The condition 40% of A = two-thirds of B gives 0.4A = 2B/3, so A/B = (2/3)/0.4 = (2/3)/(2/5)…

• A. 2 : 3 : 4
• B. 6 : 7 : 8
• C. 6 : 8 : 9
• D. None of these

Explanation: Apply each increase to its corresponding ratio term: 5 x 1.40 = 7, 7 x 1.50 = 10.5, and 8 x 1.75 = 14.