The expenditure of a company on five heads A, B, C, D and E is in proportion to 3:5:7:11:? respectively. The expenditure on E is equal to the arithmetic mean of the expenditures on A and D. If the expenditure on C exceeds that on B by ₹18,000, find the total expenditure (₹) of the company
₹2,97,000
To solve the provided problem, we need to determine the ratio and relationship between the expenditures on various heads (A, B, C, D, and E) given in the question, and then calculate the company's total expenditure.
The expenditure expenses are given in proportion as 3:5:7:11:x, where x is the expenditure ratio for E. Additionally, the expenditure for E is stated to be equal to the arithmetic mean of the expenditures on A and D.
This means:
- Expenditure on E = (Expenditure on A + Expenditure on D) / 2
Let's denote the common multiple for these proportions as k. Therefore, the expenditures can be expressed as:
- A = 3k
- B = 5k
- C = 7k
- D = 11k
- E = xk
Given that the expenditure on C exceeds that on B by ₹18,000, we can write the equation as:
- 7k - 5k = 18000
Simplifying the equation:
- 2k = 18000
- k = 9000
Now we know the value of k. Next, we use the information that the expenditure on E equals the arithmetic mean of expenditures on A and D:
- E = (A + D) / 2
- xk = (3k + 11k) / 2
- xk = 14k / 2
- xk = 7k
- x = 7
Thus, the ratios become 3:5:7:11:7.
Now we can find the total expenditure by adding the individual expenditures:
- Total Expenditure = 3k + 5k + 7k + 11k + 7k
- = 33k
Substituting the value of k:
- Total Expenditure = 33 * 9000 = ₹2,97,000
Therefore, the total expenditure of the company is ₹2,97,000. The correct answer is ₹2,97,000.
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Important Questions from Ratio and Proportion
The cost of a diamond is directly proportional to the square of its weight. The cost of a 14 gm diamond is Rs. 2560. This diamond got broken down into two pieces in the ratio of 5 ∶ 9. How much loss percent is incurred due to this breakage ? (Correct to two decimal places)
Atul purchased Bread costing Rs.20 and gave a 100 rupee note to the shopkeeper. The shopkeeper gave the balance money in coins of denomination Rs.2, Rs.5 and Rs.10. If these coins are in the ratio 5 ∶ 4 ∶ 1, then how many Rs.5 coins did the shopkeeper give?
A person divides a certain amount among his three sons in the ratio of 3 ∶ 4 ∶ 5. If he had divided this amount in the ratio of 1/3,1/4,1/5, his son, who had got the lowest share earlier, would get Rs.1,188 more. Find the amount (in Rs).
In a school 3/8 of the number of students are girls and the rest are boys. One-third of the number of boys are below 10 years and 2/3 the number if girls are also below 10 years. If the number of students of age 10 or more years is 260. then the number of boys in the school is:
If a : b : c = \(\frac{1}{4} : \frac{1}{3} : \frac{1}{2}, \) then \( \ \frac{a}{b} : \frac{b}{c} : \frac{c}{a} = ?\)
