Question
The cost of diamond varies directly as the square of its weight. A diamond broke into four pieces with weights in the ratio 1 : 3 : 4 : 7. if the loss in the total value of the diamond was Rs. 90,000. The price of the original diamond was?
Solution
Let the weight of the pieces of diamond be x, 3x, 4x, 7x Total weight of diamond = x + 3x + 4x + 7x = 15x Price ∝ (weight)2 => Price = k(weight)2 ; where, K is constant Original price = k(15x)2 Price of pieces = (kx2 + 9kx2 + 16kx2 + 49kx2) = 75kx2 Loss in price = 225kx2 – 75kx2 = 150kx2 which is given as 90,000 => 150kx2 = 90000 => kx2 = 600 Original price = 225kx2 = 225 x 600 = 135000
More Ratio and proportion Questions
- The ratio between two numbers is 6:7. If each number is increased by 9, the ratio between then become 9:10, find the difference between numbers.
- In a class, the ratio of students who passed to those who failed is 5:6. If 30 additional students had passed the exam, the ratio would shift to 17:16. How...
- Rs 2106 was divided among Anil, Bhanu and Charan in the ratio of 13:10:16 respectively. Find the amount received by Anil and Bhanu together.
- The ratio of males and females in a zoo is 4:5 respectively and the percentage of children among males and the percentage of children among females are 15%...
- The ratio of the monthly income of ‘A’ and ‘B’ is 11:13. If ‘A’ and ‘B’ save Rs. 4000 and Rs. 5000 respectively, and the ratio of their expenditure is 3:4,...
- A sum of Rs. 178 needs to be divided among 60 students in a class, where each boy receives Rs. 2.5 and each girl receives Rs. 3.5. Determine the ratio of b...
- Two numbers are in the ratio 7:5. After adding 2 and 4 to them respectively the ratio becomes 2:3. Find the bigger number.
- If the third proportion of 25 and 20 is “0.5k”, then find the value of (k − 8) : (k + 24).
- A sum of money is divided among P, Q, R and S in the ratio of 2:3:9:10 respectively. If the share of R's is Rs. 3900 more than the share of Q, then what is...
- What is the fourth proportional to 3, 8, 15?
Relevant for Exams:
