A father distributed two different amounts among his sons P, Q, R and S. First amount was distributed in the ratio 5 : 4 : 3 : 2 and the second amount was distributed in the ratio 6 : 7 : 8 : 9. If the second amount is thrice the first amount, then which son will get the maximum amount?
S
To solve this problem, we need to determine which son gets the maximum amount when two amounts are distributed among the sons P, Q, R, and S based on given ratios.
Step 1: Understanding the ratios
- The first amount is distributed in the ratio \(5 : 4 : 3 : 2\).
- The second amount is distributed in the ratio \(6 : 7 : 8 : 9\).
- The second amount is three times the first amount.
Step 2: Let the first amount be \(x\)
- The second amount is therefore \(3x\).
Step 3: Calculating the distribution for the first amount
- Total parts in the first ratio: \(5 + 4 + 3 + 2 = 14\).
- The shares from the first amount are calculated as follows:
- Share of P from first amount = \(\frac{5}{14}x\)
- Share of Q from first amount = \(\frac{4}{14}x\)
- Share of R from first amount = \(\frac{3}{14}x\)
- Share of S from first amount = \(\frac{2}{14}x\)
Step 4: Calculating the distribution for the second amount
- Total parts in the second ratio: \(6 + 7 + 8 + 9 = 30\).
- The shares from the second amount are calculated as follows:
- Share of P from second amount = \(\frac{6}{30} \times 3x = \frac{18}{30}x\)
- Share of Q from second amount = \(\frac{7}{30} \times 3x = \frac{21}{30}x\)
- Share of R from second amount = \(\frac{8}{30} \times 3x = \frac{24}{30}x\)
- Share of S from second amount = \(\frac{9}{30} \times 3x = \frac{27}{30}x\)
Step 5: Total shares for each son
- Total for P = \(\frac{5}{14}x + \frac{18}{30}x\)
- Total for Q = \(\frac{4}{14}x + \frac{21}{30}x\)
- Total for R = \(\frac{3}{14}x + \frac{24}{30}x\)
- Total for S = \(\frac{2}{14}x + \frac{27}{30}x\)
Step 6: Simplifying and comparing the totals
- To compare, calculate each total and it becomes evident:
- Total for S is \(\frac{2}{14}x + \frac{27}{30}x\)
- Total for S calculation yields a greater number compared to others when simplified, hence S gets the maximum amount.
Conclusion:
Based on the calculated totals, son S receives the maximum amount. Therefore, the correct answer is S.
Similar Questions
A sum of ₹420 is divided among A, B, C, and D such that: A : B = 4 : x, B : C = x : 7, C : D = 6 : (x − 3). If B and C together get ₹210, find the value of x.
Given the ratio 3:4::6:8, which operation verifies the proportion?
A workshop mixes coolant concentrate and water in a 3:2 ratio for a machine cooling system. If the total mixture required is 25 liters, how many liters of coolant concentrate are required?
P, Q and R are three batsmen. The ratios of runs scored by them in a certain match were as follows:
P : Q = 5 : 7 and Q : R = 2 : 3.
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- If 3 dozen guavas cost ₹ 90, how many guavas can be bought for ₹ 240?
Important Questions from Ratio and proportion
A’s marks in Mathematics are directly proportional to practice time. In 6 hours of practice, A gets 70 marks. What should be the practice time (approximately) to get 90 marks?
The average of the areas of 2 similar triangles is 706.5 m2 whose perimeters are in the ratio of 6 : 11. What is 20% of the difference (in m2) in areas of both triangles?
In a triangle ABC, D and E are two points on sides AB and AC, respectively, such that DE is parallel to BC and AD : DB = 3 : 5. If AC = 5.6 cm, then find the value (in cm) of AE.
In a triangle ABC, P and Q are two points on AB and AC, respectively, such that PQ is parallel to BC. If AC = 5QC, then the ratio PQ : BC is equal to:
Find the mean proportional between 25 and 81.
