Initial Milk = (4/5) * 45 = 36 L. Initial Water = (1/5) * 45 = 9 L. Let x liters of water be added. New ratio: 36 / (9 + x) = 3 / 2. Cross-multiplying: 72 = 27 + 3x => 3x = 45 => x = 15 L.
7312
Seats for Mathematics, Physics, and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50%, and 75% respectively. What will be the ratio of increased seats?
Let seats be 50, 70, 80. New seats for Math = 50 * 1.40 = 70. New Physics = 70 * 1.50 = 105. New Biology = 80 * 1.75 = 140. New ratio = 70 : 105 : 140. Dividing by 35 gives 2 : 3 : 4.
7313
The ratio of the present ages of a mother and daughter is 7 : 1. Four years ago, the ratio of their ages was 19 : 1. What will be the mother's age four years from now?
Let present ages be 7x and x. 4 years ago: (7x - 4) / (x - 4) = 19 / 1. 7x - 4 = 19x - 76 => 12x = 72 => x = 6. Present age of mother = 7(6) = 42. Mother's age 4 years from now = 42 + 4 = 46 years.
7314
A box contains Rs. 56 in the form of coins of one rupee, 50 paise, and 25 paise. The number of 50 paise coins is double the number of 25 paise coins and four times the number of one rupee coins. How many 50 paise coins are there?
Let the number of 1 Re coins be x. Then 50p coins = 4x, and 25p coins = 2x. Value: 1(x) + 0.5(4x) + 0.25(2x) = 56. => x + 2x + 0.5x = 56 => 3.5x = 56 => x = 16. The number of 50 paise coins is 4x = 4 * 16 = 64.
7315
A, B, and C enter into a partnership. A invests 3 times as much as B, and B invests two-thirds of what C invests. At the end of the year, the profit earned is Rs. 6600. What is B's share?
Let C's investment be 3x. Then B's investment is (2/3)*3x = 2x. A's investment is 3*(2x) = 6x. The ratio of investments A : B : C = 6x : 2x : 3x = 6 : 2 : 3. Total parts = 11. B's share = (2/11) * 6600 = 2 * 600 = Rs. 1200.
We have 0.75x = 0.5y. Converting to fractions: (3/4)x = (1/2)y. Multiplying both sides by 4 gives 3x = 2y. Therefore, x / y = 2 / 3, which is 2 : 3.
7317
A sum of Rs. 427 is to be divided among A, B, and C such that 3 times A's share, 4 times B's share, and 7 times C's share are all equal. Find the share of C.
Given 3A = 4B = 7C = k. A = k/3, B = k/4, C = k/7. Ratio A : B : C = 1/3 : 1/4 : 1/7. LCM of 3, 4, 7 is 84. Multiply by 84 to get 28 : 21 : 12. Total parts = 28 + 21 + 12 = 61 parts. C's share = (12 / 61) * 427 = 12 * 7 = Rs. 84.
7318
Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?
Let their salaries be 2x and 3x. (2x + 4000) / (3x + 4000) = 40 / 57. Cross-multiplying: 57(2x + 4000) = 40(3x + 4000) => 114x + 228000 = 120x + 160000 => 6x = 68000 => x = 11333.33. Sumit's salary is 3x = 3 * 11333.33 = Rs. 34000. Wait, 68000/6 = 11333.33. Let's re-solve: 114x+228k = 120x+160k. 6x = 68000. x = 34000/3. 3x = 34000. Option D is 38000. Recalculate: 57*4000 = 228,000. 40*4000 = 160,000. 228k - 160k = 68k. 6x = 68k. Sumit is 3x, so 3x = 34000. Oh, the options are wrong in my draft. I will correct the explanation and answer. Let's assume standard values. If x=17000, 2x=34000, 3x=51000. Let's choose the correct answer mathematically. I will replace option D with Rs. 34000.
7319
The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls is 20% and 10% respectively, what will be the new ratio?
Let the number of boys and girls be 70 and 80. New number of boys = 70 * 1.20 = 84. New number of girls = 80 * 1.10 = 88. The new ratio is 84 : 88. Dividing by 4 gives 21 : 22.
7320
Rs. 1210 were divided among A, B, and C such that A : B = 5 : 4 and B : C = 9 : 10. What is C's share?
Make B common: A : B = 5*9 : 4*9 = 45 : 36. B : C = 9*4 : 10*4 = 36 : 40. Thus, A : B : C = 45 : 36 : 40. Total parts = 45 + 36 + 40 = 121. Value of 1 part = 1210 / 121 = 10. C's share = 40 * 10 = Rs. 400.
