Ratio and proportion
- 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
- If A : B = 2 : 3 and B : C = 4 : 5, and A + B + C = 700, find C. Answer: C. 300 Answer: (C) 300 Make B equal: A : B = 8 : 12, B : C = 12 : 15, so A : B : C = 8 : 12 : 15 (total 35). C = 15/35 × 700 = 300 . 1