Read each question, consider the options, then reveal the correct answer and explanation.
100 MCQs10 per page8 of 10
MCQ 71Ratio And Proportion
In an examination, the number passing is four times the number failing. If there had been 35 fewer candidates and 9 more failures, passed:failed would be 2:1. Find the original total.
135
155
145
150
Correct answerB — 155
Explanation
Let failures=x and passes=4x, so total=5x. Under the hypothetical condition, failures become x+9 and passes become 4x−44 because total falls by 35 while 9 more fail. Then (4x−44)/(x+9)=2. Solving gives 2x=62, x=31, and total=155.
Write the percentages as fractions: 26%=26/100 and 38%=38/100. The expression becomes 12×26×5×38×7×10000 divided by 100×78×100×152. Extensive cancellation leaves 35. Cancelling before multiplying avoids large intermediate values.
MCQ 73Work And Wages
A, B, and C can complete a work in 20, 24, and 30 days, respectively. They undertake it for ₹5400. They start together, but B leaves 2 days before completion and C leaves 5 days before completion. What is A's share?
₹2700
₹540
₹1800
₹600
Correct answerA — ₹2700
Explanation
Let total duration be x days. Work completed is x/20+(x−2)/24+(x−5)/30=1. Multiplying by 120 gives 6x+5x−10+4x−20=120, so x=10. A works all 10 days and completes 10/20=1/2 of the work. Therefore A receives half of ₹5400 = ₹2700.
MCQ 74Average
The average temperature over four days is 48°C. The average of the second and third days is 34°C, and the first and fourth temperatures are in the ratio 9:11. What were the first and fourth temperatures?
55.8°C and 68.2°C
43.4°C and 68.2°C
45.5°C and 49.9°C
52.4°C and 46.8°C
Correct answerA — 55.8°C and 68.2°C
Explanation
The four-day total is 192°C. The second and third days total 68°C, leaving 124°C for the first and fourth days. Dividing 124 in the ratio 9:11 gives 55.8°C and 68.2°C. The source options contained a misprinted first temperature.
MCQ 75Percentage
In 1998, students taking examinations in states X, Y, and Z were in the ratio 3:5:6. Next year they rose by 20%, 10%, and 20%. If X:Z next year is 1:2, how many students took the examination in 1998?
5000
Cannot be determined from the data
6000
75000
Correct answerB — Cannot be determined from the data
Explanation
The original X:Z ratio is 3:6 = 1:2. Both X and Z then rise by the same 20%, so their ratio remains 1:2 for every possible scale of the original ratio. No absolute total is given, so the number of students cannot be determined.
MCQ 76Partnership
Amitabh, Brijesh, and Kamlesh initially invest in the ratio 7/2 : 4/3 : 6/5. After 4 months Amitabh increases his capital by 50%. If annual profit is ₹21600, what is Brijesh's share?
₹8000
₹4000
₹12000
₹7000
Correct answerB — ₹4000
Explanation
Multiplying the initial fractional ratio by 30 gives 105:40:36. Amitabh's capital-time value is 105×4 + 157.5×8 = 1680; Brijesh's is 40×12=480; Kamlesh's is 36×12=432. The ratio is 35:10:9. Brijesh receives 10/54×21600 = ₹4000.
MCQ 77Discount
Selling an article at 80% of marked price gives a 10% loss. What profit percentage results if it is sold at 95% of marked price?
5%
5.9%
12.5%
6.875%
Correct answerD — 6.875%
Explanation
At 80% of marked price, selling price equals 90% of cost price. Therefore MP = 0.90/0.80 = 1.125 times cost price. At 95% of MP, selling price is 0.95×1.125 = 1.06875 times cost price, giving 6.875% profit, approximately 6.9%.
MCQ 78Simple And Decimal Fractions
Three fractions have sum 2 11/24. The greatest divided by the smallest is 7/6, and 7/6 exceeds the middle fraction by 1/3. What are the fractions in descending order?
3/5, 4/7, 2/3
7/9, 2/3, 3/5
7/8, 5/6, 3/4
7/8, 7/9, 7/10
Correct answerC — 7/8, 5/6, 3/4
Explanation
Let greatest=x, middle=y, smallest=z. From 7/6 being 1/3 greater than y, y=7/6-1/3=5/6. Also x/z=7/6, so x=7z/6. The sum is 59/24. Solving 7z/6 + 5/6 + z = 59/24 gives z=3/4, hence x=7/8. Thus the fractions are 7/8, 5/6, 3/4.
MCQ 79Average
Sections A, B, C, and D have average weights 45, 50, 72, and 80 kg, and their combined average is 60 kg. A+B together average 48 kg and B+C together average 60 kg. What is the ratio of student numbers in A and D?
3:2
8:5
4:3
12:7
Correct answerC — 4:3
Explanation
Let section sizes be a,b,c,d. From A+B average 48, 45a+50b=48(a+b), giving 3a=2b. From B+C average 60, 50b+72c=60(b+c), giving 10b=12c. Using the overall average equation and these relations simplifies to 15a=20d, so d=4:3.
MCQ 80Discount
On the same marked price, a 30% discount and successive discounts of 20% and 10% produce selling prices differing by ₹72. What is the marked price?
₹3000
₹2500
₹3600
₹2400
Correct answerC — ₹3600
Explanation
A 30% discount leaves 70% of the marked price. Successive discounts of 20% and 10% leave 0.80×0.90 = 72% of the marked price. The selling-price difference is therefore 2% of the marked price. Hence 0.02M = 72 and M = ₹3600.
