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What is the mean proportional between 9 and 64? Answer: C. 24 Answer: (C) 24 Mean proportional = √(9 × 64) = √(576) = 24 . Ratio and proportion 1 answer
In the following question, two equations numbered I and II are given. Solve both equations and choose the correct relationship between x and y.I. \( 2x^2 - 11x + 15 = 0 \)II. \( 3y^2 - 8y + 4 = 0 \) Answer: A. x > y Answer: (A) x > y I gives x = 2.5, 3. II gives y = 0.67, 2. Comparing every pair of values: x > y. Quadratic equations 1 answer
In the following question, two equations numbered I and II are given. Solve both equations and choose the correct relationship between x and y.I. \( x^2 - 4x + 4 = 0 \)II. \( y^2 - 5y + 6 = 0 \) Answer: C. x ≤ y Answer: (C) x ≤ y I gives x = 2. II gives y = 2, 3. Comparing every pair of values: x ≤ y. Quadratic equations 1 answer
In the following question, two equations numbered I and II are given. Solve both equations and choose the correct relationship between x and y.I. \( x^2 + 11x + 30 = 0 \)II. \( y^2 + 13y + 42 = 0 \) Answer: B. x ≥ y Answer: (B) x ≥ y I gives x = -6, -5. II gives y = -7, -6. Comparing every pair of values: x ≥ y. Quadratic equations 1 answer
The table shows the total number of students enrolled in five coaching centres (P to T) and the percentage of girls among them. Study it and answer the question.CentreTotal studentsGirls (%)P60040%Q75052%R48045%S90038%T52055%How many boys are enrolle… Answer: C. 558 Answer: (C) 558 Boys = 62% of 900 = 558. Data interpretation 1 answer
The table shows the total number of students enrolled in five coaching centres (P to T) and the percentage of girls among them. Study it and answer the question.CentreTotal studentsGirls (%)P60040%Q75052%R48045%S90038%T52055%What is the total number… Answer: B. 456 Answer: (B) 456 P: 40% of 600 = 240. R: 45% of 480 = 216. Total = 456. Data interpretation 1 answer
The table shows the total number of students enrolled in five coaching centres (P to T) and the percentage of girls among them. Study it and answer the question.CentreTotal studentsGirls (%)P60040%Q75052%R48045%S90038%T52055%What is the ratio of the… Answer: D. 5 : 3 Answer: (D) 5 : 3 Girls in Q = 52% of 750 = 390. Boys in T = 45% of 520 = 234. 390 : 234 = 5 : 3. Data interpretation 1 answer
The table shows the total number of students enrolled in five coaching centres (P to T) and the percentage of girls among them. Study it and answer the question.CentreTotal studentsGirls (%)P60040%Q75052%R48045%S90038%T52055%What is the average numbe… Answer: B. 650 Answer: (B) 650 Total = 600 + 750 + 480 + 900 + 520 = 3250. Average = 3250 ÷ 5 = 650. Data interpretation 1 answer
The table shows the total number of students enrolled in five coaching centres (P to T) and the percentage of girls among them. Study it and answer the question.CentreTotal studentsGirls (%)P60040%Q75052%R48045%S90038%T52055%The number of girls in ce… Answer: A. 32.41% Answer: (A) 32.41% Girls in T = 55% of 520 = 286; girls in R = 216. 286-216/216 × 100 = 70/216 × 100 ≈ 32.41% . (24.48% us... Data interpretation 1 answer
Ramesh spends 65% of his salary and saves the rest. His salary increases by 20% and his expenditure increases by 10%. By approximately what percent do his savings increase? Answer: A. 38.57% Answer: (A) 38.57% Take salary 100: expenditure 65, savings 35. New salary 120, new expenditure 71.5, new savings 48.5. In... Percentage 1 answer
The ratio of boys to girls in a class is 4 : 5. When 8 more boys join the class, the numbers of boys and girls become equal. How many girls are there in the class? Answer: B. 40 Answer: (B) 40 4k + 8 = 5k gives k = 8. Girls = 5 × 8 = 40. Ratio and proportion 1 answer
The average weight of 20 students is 45 kg. When the teacher's weight is included, the average increases by 1 kg. What is the teacher's weight (in kg)? Answer: B. 66 Answer: (B) 66 New total = 21 × 46 = 966 kg; old total = 900 kg. Teacher = 66 kg. Average 1 answer
By selling an article for Rs. 1,512, a shopkeeper gains 12%. At what price (in Rs.) should he sell it to gain 20%? Answer: C. 1620 Answer: (C) 1620 CP = 1512 ÷ 1.12 = Rs. 1,350. For 20% gain, SP = 1350 × 1.2 = Rs. 1,620. Profit, loss and discount 1 answer
An article is marked at Rs. 2,500. Two successive discounts of 20% and 10% are given on it. What is the selling price (in Rs.)? Answer: D. 1800 Answer: (D) 1800 SP = 2500 × 0.80 × 0.90 = Rs. 1,800. (A single 30% discount would wrongly give Rs. 1,750.) Profit, loss and discount 1 answer
A sum of money lent at simple interest amounts to Rs. 7,800 in 3 years and to Rs. 9,000 in 5 years. What is the rate of interest per annum? Answer: B. 10% Answer: (B) 10% Interest for 2 years = 9000 − 7800 = 1200, so Rs. 600 per year. Principal = 7800 − 3 × 600 = 6000. Rate = 600... Simple and compound interest 1 answer
What is the compound interest on Rs. 16,000 at 10% per annum for 3 years, compounded annually (in Rs.)? Answer: C. 5296 Answer: (C) 5296 Amount = 16000 × (1.1)³ = 21296 . CI = 21296 − 16000 = Rs. 5,296. Simple and compound interest 1 answer
A, B and C start a business with Rs. 20,000, Rs. 30,000 and Rs. 45,000 respectively. After 6 months, A adds Rs. 10,000 more. Out of a profit of Rs. 48,000 at the end of the year, what is A's share (in Rs.)? Answer: C. 12000 Answer: (C) 12000 A: 20000 × 6 + 30000 × 6 = 300000; B: 30000 × 12 = 360000; C: 45000 × 12 = 540000. Ratio = 5 : 6 : 9. A's... Partnership 1 answer
In what ratio must rice costing Rs. 42 per kg be mixed with rice costing Rs. 54 per kg so that the mixture costs Rs. 46 per kg? Answer: D. 2 : 1 Answer: (D) 2 : 1 By alligation: (54 − 46) : (46 − 42) = 8 : 4 = 2 : 1. Mixture and alligation 1 answer
A and B together can finish a work in 12 days, B and C in 15 days, and C and A in 20 days. In how many days can A, B and C together finish it? Answer: C. 10 Answer: (C) 10 2(A + B + C) = 1/12+1/15+1/20 = 12/60 = 1/5 . So A + B + C = 1/10 : 10 days. Time and work 1 answer
A pipe can fill a tank in 8 hours. Because of a leak at the bottom, it takes 10 hours to fill the tank. In how many hours can the leak alone empty the full tank? Answer: B. 40 Answer: (B) 40 Leak rate = 1/8 - frac110 = 1/40 . The leak empties the tank in 40 hours. Pipes and cisterns 1 answer
Two trains, 150 m and 210 m long, run on parallel tracks in opposite directions at 45 km/h and 63 km/h. How many seconds do they take to cross each other completely? Answer: A. 12 Answer: (A) 12 Relative speed = 108 km/h = 30 m/s. Distance = 150 + 210 = 360 m. Time = 360 ÷ 30 = 12 s. Time, speed and distance 1 answer
The speed of a boat in still water is 15 km/h and the speed of the stream is 3 km/h. The boat goes 36 km downstream and comes back to the starting point. What is the total time taken (in hours)? Answer: C. 5 Answer: (C) 5 Downstream speed = 18 km/h (2 h), upstream speed = 12 km/h (3 h). Total = 5 hours. Boats and streams 1 answer
The sum of the present ages of a father and his son is 56 years. Four years ago, the father's age was three times the son's age. What is the father's present age (in years)? Answer: B. 40 Answer: (B) 40 F + S = 56 and F − 4 = 3(S − 4), so F = 3S − 8. Then 4S − 8 = 56, S = 16 and F = 40 years. Ages 1 answer
Two fair dice are thrown together. What is the probability that the sum of the numbers on them is 8? Answer: C. 5/36 Answer: (C) 5/36 Favourable outcomes: (2,6), (3,5), (4,4), (5,3), (6,2) = 5 out of 36. Probability = 5/36. Probability 1 answer

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