Arithmetic questions
Ratios (3 Questions) in NMAT 2024
Q1. The ratio of incomes of A and B is 3:4, and their expenses are in the ratio 2:3. If both save ₹6,000, what is A’s income?
A) ₹18,000 B) ₹24,000 C) ₹21,000 D) ₹27,000
Q2. The ratio of boys to girls in a class is 5:3. If 8 more girls join, the ratio becomes 5:4. How many boys are there?
A) 40 B) 50 C) 45 D) 60
Q3. Two numbers are in the ratio 7:9. If the difference between them is 16, what is the larger number?
A) 56 B) 64 C) 72 D) 80
Percentages (3 Questions) in NMAT 2024
Q4. A number is increased by 20% and then decreased by 20%. What is the net percentage change?
A) 4% increase B) 4% decrease C) 0% D) 2% decrease
Q5. A student scored 40% in Paper A and 60% in Paper B. If both papers are of equal weight, what is his average percentage?
A) 48% B) 50% C) 52% D) 55%
Q6. An article is sold at ₹960 after giving a discount of 20%. What is the marked price?
A) ₹1,000 B) ₹1,100 C) ₹1,150 D) ₹1,200
Averages (2 Questions) in NMAT 2024
Q7. The average of 6 numbers is 25. If one number is removed, the average becomes 24. What number was removed?
A) 30 B) 36 C) 34 D) 40
Q8. The average marks of 20 students in a class is 65. Later it was found that one mark was wrongly entered as 85 instead of 45. What is the correct average?
A) 63 B) 64 C) 62 D) 61
Mixtures (2 Questions) in NMAT 2024
Q9. In what ratio should water be mixed with milk costing ₹24/litre so that the selling price of ₹20/litre gives a profit of 25%?
A) 1:3 B) 1:2 C) 1:1 D) 2:3
Q10. A 60-litre mixture contains milk and water in the ratio 2:1. How much water must be added to make the ratio 1:1?
A) 20 L B) 30 L C) 15 L D) 10 L
Answers and detailed explanations in NMAT 2024
Ratios NMAT 2024
Q1. Answer: A) ₹18000
Explanation:
Let incomes of A and B be 3x and 4x; expenses be 2y and 3y.
Savings A = 3x – 2y = 6000
Savings B = 4x – 3y = 6000
Subtract equations:
(4x – 3y) – (3x – 2y) = 0 → x = y
Substitute in A’s income: 3x – 2x = 6000 → x = 6000
A’s income = 3x = ₹18,000
x = ₹6000 → A’s income = 3×6000 = ₹18,000
Q2. Answer: A) 40
Explanation:
Let boys = 5x, girls = 3x
After 8 girls join → girls = 3x + 8
New ratio = 5x : (3x + 8) = 5:4
Cross-multiply: 5(3x + 8) = 4×5x → 15x + 40 = 20x → 5x = 40 → x = 8
Boys = 5x = 40
Answer: A) 40
Q3. Answer: C) 72
Explanation:
Let numbers = 7x, 9x → Difference = 2x = 16 → x = 8
Larger number = 9x = 72
Percentages NMAT 2024
Q4. Answer: B) 4% decrease
Explanation:
Let original = 100
Increase 20% → 120
Then decrease 20% → 120 × 0.8 = 96
Change = 100 – 96 = 4% decrease
Q5. Answer: B) 50%
Explanation:
Average = (40 + 60)/2 = 50%
Q6. Answer: D) ₹1,200
Explanation:
Let marked price = x
Discount 20% → SP = 80% of x = 0.8x = 960 → x = 960 / 0.8 = ₹1,200
Averages NMAT 2024
Q7. Answer: A) 30
Explanation:
Total of 6 = 6×25 = 150
New total = 5×24 = 120
Removed number = 150 – 120 = 30
Answer: A) 30
Q8. Answer: A) 63
Explanation:
Wrong total = 20×65 = 1300
Correct total = 1300 – 85 + 45 = 1260
Correct avg = 1260 / 20 = 63
Answer: A) 63
Mixtures NMAT 2024
Q9. Answer: B) 1:2
Explanation:
SP = ₹20, Profit = 25% → CP = 20 / 1.25 = ₹16
Let water added be w litres to 1 litre milk
(24×1 + 0×w)/(1 + w) = 16 → 24/(1 + w) = 16
1 + w = 24/16 = 1.5 → w = 0.5
Ratio water:milk = 0.5:1 = 1:2
Q10. Answer: A) 20 L
Explanation:
Milk:Water = 2:1 → in 60L → 40L milk, 20L water
To make it 1:1, water must be 40L → add 20L more
20 – 20 = 20 → Add 20 L water
Answer: A) 20 L
Final Answer Key of NMAT 2024
Q1: A
Q2: A
Q3: C
Q4: B
Q5: B
Q6: D
Q7: A
Q8: A
Q9: B
Q10: A
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