Government exams
- The incomes of A and B are in the ratio 5 : 4 and their expenditures are in the ratio 3 : 2. If each of them saves ₹1,600, what is A's income? Answer: D. ₹4000 Answer: (D) ₹4000 Let incomes be 5x, 4x and expenditures 3y, 2y. Then 5x − 3y = 1600 and 4x − 2y = 1600. From the second, y... 1
- A bag contains ₹1, 50-paise and 25-paise coins in the ratio 5 : 6 : 8. The total value is ₹210. How many 50-paise coins are there? Answer: B. 126 Answer: (B) 126 Shortcut: convert the number ratio into a value ratio: 5 × 1 : 6 × 0.5 : 8 × 0.25 = 5 : 3 : 2, i.e. 10 value... 1
- What number must be added to each of 6, 10, 14 and 22 so that the resulting numbers are in proportion? Answer: A. 2 Answer: (A) 2 Let x be added. Then (6 + x)(22 + x) = (10 + x)(14 + x). 132 + 28x = 140 + 24x, so 4x = 8 and x = 2. Check: 8 : 1... 1
- Two numbers are in the ratio 3 : 5. If 10 is added to each, the ratio becomes 5 : 7. What is the smaller number? Answer: A. 15 Answer: (A) 15 Let the numbers be 3k and 5k. Then 7(3k + 10) = 5(5k + 10), so 21k + 70 = 25k + 50 and k = 5. Smaller number =... 1
- A 40-litre mixture contains milk and water in the ratio 3 : 1. How much water must be added to make the ratio 3 : 2? Answer: C. 10 litres Answer: (C) 10 litres Milk = 30 L, water = 10 L. Milk does not change, so for 3 : 2 water must be 30 × 2/3 = 20 L. Wate... 1
- The salaries of A, B and C are in the ratio 2 : 3 : 5. If their salaries are increased by 15%, 10% and 20% respectively, what is the new ratio? Answer: B. 23 : 33 : 60 Answer: (B) 23 : 33 : 60 New salaries: 2 × 1.15 : 3 × 1.10 : 5 × 1.20 = 2.3 : 3.3 : 6. Multiply by 10: 23 : 33 : 60. 1
- If x : y = 3 : 4, what is (4x + 5y) : (5x − 2y)? Answer: D. 32 : 7 Answer: (D) 32 : 7 Shortcut: put x = 3, y = 4. 4x + 5y = 12 + 20 = 32 and 5x − 2y = 15 − 8 = 7. Ratio = 32 : 7. 1
- ₹3,400 is divided among A, B and C such that A gets \(\frac{2}{3}\) of what B gets and B gets \(\frac{1}{4}\) of what C gets. What is C's share? Answer: C. ₹2400 Answer: (C) ₹2400 Take C = 12 (LCM-friendly). Then B = 12 ÷ 4 = 3 and A = 2/3 × 3 = 2. So A : B : C = 2 : 3 : 12 (17 parts)... 1
- Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, the ratio becomes 12 : 23. What is the smaller number? Answer: B. 33 Answer: (B) 33 Let the numbers be 3k and 5k. Then 23(3k − 9) = 12(5k − 9). 69k − 207 = 60k − 108, so 9k = 99 and k = 11. Small... 1
- ₹6,500 is divided among A, B and C in the ratio \(\frac{1}{2} : \frac{1}{3} : \frac{1}{4}\). What is B's share? Answer: D. ₹2000 Answer: (D) ₹2000 Multiply by the LCM 12: the ratio becomes 6 : 4 : 3, a total of 13 parts. 1 part = 6500 ÷ 13 = 500. B's s... 1
- The numbers of students in three sections are in the ratio 3 : 5 : 7. If 15 students are added to each section, the ratio becomes 3 : 4 : 5. How many students were there in all at first? Answer: D. 75 Answer: (D) 75 Let the sections have 3k, 5k, 7k. From the first two: 4(3k + 15) = 3(5k + 15), so 12k + 60 = 15k + 45 and k = 5... 1
- If (a + b) : (a − b) = 7 : 3, what is a : b? Answer: C. 5 : 2 Answer: (C) 5 : 2 Shortcut (componendo–dividendo): a : b = (7 + 3) : (7 − 3) = 10 : 4. So a : b = 5 : 2. 1
- The fares for first class and second class between two stations are in the ratio 4 : 1, and the numbers of passengers travelling in them are in the ratio 1 : 40. If the total money collected is ₹1,320, how much was collected from first-class passenge… Answer: B. ₹120 Answer: (B) ₹120 Collection = fare × passengers. Ratio of collections = 4 × 1 : 1 × 40 = 4 : 40 = 1 : 10 (11 parts). 1 part... 1
- The seats for Mathematics, Physics and Biology in a college are in the ratio 4 : 5 : 6. It is proposed to increase them by 50%, 20% and 25% respectively. What will be the new ratio? Answer: D. 4 : 4 : 5 Answer: (D) 4 : 4 : 5 New seats: 4 × 1.5 : 5 × 1.2 : 6 × 1.25 = 6 : 6 : 7.5. Multiply by 2 and divide by 3: 12 : 12 : 1... 1
- x varies directly as y and inversely as the square of z. When y = 4 and z = 2, x = 3. What is x when y = 18 and z = 3? Answer: A. 6 Answer: (A) 6 x = ky/z² . From 3 = k × 4 ÷ 4, k = 3. So x = 3 × 18 ÷ 9 = 6. Trap: dividing by z instead of z² gives k = 1.5 and... 1
- ₹1,210 is divided among A, B and C such that A : B = 5 : 4 and B : C = 9 : 10. What is C's share? Answer: A. ₹400 Answer: (A) ₹400 Make B common: A : B = 45 : 36 and B : C = 36 : 40, so A : B : C = 45 : 36 : 40 (121 parts). 1 part = 1210... 1
- Two alloys contain gold and copper in the ratios 7 : 2 and 7 : 11. Equal weights of the two alloys are melted together. What is the ratio of gold to copper in the new alloy? Answer: A. 7 : 5 Answer: (A) 7 : 5 Take 18 kg of each (LCM of 9 and 18). First alloy: gold 14 kg, copper 4 kg. Second alloy: gold 7 kg, copp... 1
- An article is sold at a loss of 10%. Had it been sold for ₹90 more, there would have been a gain of 5%. What is the cost price? Answer: C. ₹600 Answer: (C) ₹600 Shortcut: the gap between −10% and +5% is 15% of CP = ₹90. CP = 90 × 100 ÷ 15 = ₹600. 1
- An article costs ₹400. At what price must it be marked so that after a discount of 20% the shopkeeper still gains 20%? Answer: D. ₹600 Answer: (D) ₹600 Required SP = 1.2 × 400 = ₹480. SP is 80% of MP, so MP = 480 ÷ 0.8 = ₹600. Shortcut: MP = CP × (100 + gain)... 1
- A man sells two watches at ₹990 each. On one he gains 10% and on the other he loses 10%. What is his overall result? Answer: D. A loss of 1% Answer: (D) A loss of 1% Shortcut: when two items are sold at the same SP with x% gain and x% loss, there is always... 1
- After giving a discount of 10%, a trader still makes a profit of 25%. What is the ratio of the marked price to the cost price? Answer: B. 25 : 18 Answer: (B) 25 : 18 SP = 0.9 × MP = 1.25 × CP, so MP/CP = 1.25/0.9 = 125/90 = 25/18 . MP : CP = 25 : 18. 1
- A shop offers "Buy 4, get 1 free". What is the effective discount percent? Answer: C. 20% Answer: (C) 20% The customer gets 5 items for the price of 4. Discount = 1 item out of 5 = 20%. Trap: 1/4 = 25% divides by th... 1
- A shopkeeper cheats by 20% both while buying and while selling: he takes 20% more goods than he pays for, and gives 20% less than he charges for. What is his overall profit percent? Answer: B. 50% Answer: (B) 50% For ₹100 he receives 120 units of goods. He sells each 80 units as if they were 100. So 120 units bring 120 ×... 1
- The profit earned by selling an article for ₹1,060 equals the loss incurred by selling it for ₹860. At what price should it be sold to make a 25% profit? Answer: D. ₹1200 Answer: (D) ₹1200 Shortcut: CP is midway between the two SPs: (1060 + 860) ÷ 2 = ₹960. SP for 25% profit = 1.25 × 960 = ₹12... 1