Question
- A sum is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paise and Z gets 30 paise. If the share of Y is Rs 27, what is the total amount?
Answer: Option C
Let the amount X gets be Rs. x.
Then, Y gets 45/100 of x = 9/20 of x and Z gets 30/100 of x = 3/10 of x.
Given, Y gets Rs. 27.
So, 9/20 of x = 27
⇒ x = (27 × 20)/9 = Rs. 60
Total amount = Rs. (x + 9/20x + 3/10x) = Rs. (60 + 27 + 18) = Rs. 105
Therefore, the correct answer is option C) Rs. 105.
Key takeaways and formulas:
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Let the amount X gets be Rs. x.
Then, Y gets 45/100 of x = 9/20 of x and Z gets 30/100 of x = 3/10 of x.
Given, Y gets Rs. 27.
So, 9/20 of x = 27
⇒ x = (27 × 20)/9 = Rs. 60
Total amount = Rs. (x + 9/20x + 3/10x) = Rs. (60 + 27 + 18) = Rs. 105
Therefore, the correct answer is option C) Rs. 105.
Key takeaways and formulas:
- In a ratio distribution problem, the sum of the ratios is the total number of parts. For instance, in this problem, the sum of the ratios is 1 + 45/100 + 30/100 = 1.75, which means there are 1.75 parts in total.
- To find the share of each person, we multiply the total amount by the ratio they get. For example, if X gets x, then Y gets (45/100)x and Z gets (30/100)x.
- We can also use proportions to solve the problem. For example, if Y gets Rs. 27, we can set up the proportion (45/100)x/((9/20)x) = 27/1 and solve for x.
- The total amount is the sum of the individual shares, which is x + (45/100)x + (30/100)x.
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=> 20:13:7
Total sum be x
Y's share is rs.27
i.e)x × 9/35=27
x=105
9---27
35---?
35×27/9=105(C)