Ratio and Propotion

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

A. 2 : 5 B. 3 : 5 C. 4 : 5 D. 6 : 7 Answer: Option C Explanation: Let the third number be x. Then, first number = 120% of x = 120x = 6x 100 5 Second number = 150% of x = 150x = 3x 100 2  Ratio of first two numbers = 6x : 3x = 12x : 15x = 4 : 5. 5 2 A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share? A. Rs. 500 B. Rs. 1500 C. Rs. 2000 D. None of these Answer: Option C Explanation: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively. Then, 4x - 3x = 1000  x = 1000.  B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000. 3. 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? A. 2 : 3 : 4 B. 6 : 7 : 8 C. 6 : 8 : 9 D. None of these Answer: Option A Explanation: Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively. Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x). 140 x 5x , 150 x 7x and 175 x 8x 100 100 100  7x, 21x and 14x. 2  The required ratio = 7x : 21x : 14x 2  14x : 21x : 28x  2 : 3 : 4. 4. In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is: A. 20 litres B. 30 litres C. 40 litres D. 60 litres Answer: Option D Explanation: Quantity of milk = 60 x 2 litres = 40 litres. 3 Quantity of water in it = (60- 40) litres = 20 litres. New ratio = 1 : 2 Let quantity of water to be added further be x litres. Then, milk : water = 40 . 20 + x Now, 40 = 1 20 + x 2  20 + x = 80  x = 60.  Quantity of water to be added = 60 litres.