Calculating Share A from Money Division
The problem involves dividing a total amount of ₹28,000 among three individuals, A, B, and C, based on a specific proportional relationship between their shares.
Understanding the Share Relationship
We are given the following relationship between the shares of A, B, and C:
- $2 \times \text{Share of A} = 9 \times \text{Share of B} = 6 \times \text{Share of C}$
Let the common value of these expressions be $k$. Therefore:
- $2 \times \text{Share of A} = k \implies \text{Share of A} = \frac{k}{2}$
- $9 \times \text{Share of B} = k \implies \text{Share of B} = \frac{k}{9}$
- $6 \times \text{Share of C} = k \implies \text{Share of C} = \frac{k}{6}$
Finding the Ratio of Shares
The ratio of the shares of A, B, and C is:
$\text{Share of A} : \text{Share of B} : \text{Share of C} = \frac{k}{2} : \frac{k}{9} : \frac{k}{6}$
To simplify this ratio, we can multiply each part by the Least Common Multiple (LCM) of the denominators (2, 9, and 6). The LCM is 18.
Ratio $= \left(\frac{k}{2} \times 18\right) : \left(\frac{k}{9} \times 18\right) : \left(\frac{k}{6} \times 18\right)$
Ratio $= 9k : 2k : 3k$
Simplifying further by dividing by $k$, the ratio is $9 : 2 : 3$.
Calculating Share A
The sum of the parts in the ratio is $9 + 2 + 3 = 14$.
The total amount to be divided is ₹28,000.
Share A is $\frac{9}{14}$ of the total amount.
Share of A $= \frac{9}{14} \times ₹28,000$
Share of A $= 9 \times \frac{₹28,000}{14}$
Share of A $= 9 \times ₹2,000$
Share of A $= ₹18,000$
Similar Questions
- Which of the following ratios is the greatest?
- The ratio of the incomes of Barun and Anil is $12 : 13$ and that of their expenditures is $10 : 13$. Find the income of Barun and Anil, if they save $₹2100$ and $₹1,300$, respectively.
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- Two natural numbers are in the ratio of $6 : 8$ and their product is $768$. The smaller of the numbers is:
- Two numbers are in the ratio 2 : 3; if 20 is added to 20% of the smaller number, it will be equal to 10% of the larger number plus 25. Then, the smaller number is: _______.
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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 \( \ \frac{a}{b} : \frac{b}{c} : \frac{c}{a} = ?\)
