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25 Dec 2023, 02:30
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Difficulty:
55%
(hard)
Question Stats:
72% (03:17) correct
28%
(03:19)
wrong
based on 207
sessions
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The income of four persons are in the ratio of 7 : 4 : 8 : 10 respectively. First person spends 20% of his income second person saves 30%, 3rd person saves 40% and fourth person spends 10%. If the difference of total income of four persons and total expenditure of 4 persons is Rs 5700, what is the total income of all four persons:
(A) 7800
(B) 8300
(C) 8500
(D) 8700
(E) 8900
(A) 7800
(B) 8300
(C) 8500
(D) 8700
(E) 8900
25 Dec 2023, 05:55
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Total income = 29x
Total expense = 0.2*7x + 0.7*4x + 0.6*8x + 0.1*10x = 10x
Total income - Total expense = 5700
19x = 5700
x=300
Total income = 8700 (D IMO)
Total expense = 0.2*7x + 0.7*4x + 0.6*8x + 0.1*10x = 10x
Total income - Total expense = 5700
19x = 5700
x=300
Total income = 8700 (D IMO)
General Discussion
25 Dec 2023, 11:45
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The idea of such fraction would never be a fraction based on the option provided, we could calculate the saving or spending which ever is smaller for easier calculation. Choosing expenditure or saving results in same approach of “finding x”.
Lets take an example with the problem:
Income: 7, Expenditure: 20%, Saving: 100 - 20 = 80%. For simplicity, I'm considering expenditure here, i.e. 20% or \(\frac{2}{10}\)
Income: 4, Saving: 30%, Expenditure: 100 - 30 = 70 % or \(\frac{7}{10}\)
Income: 8, Saving 40%, Expenditure: 100-40 = 60% or \(\frac{6}{10}\)
Income: 10, Expenditure: 10%, Saving 100 - 10 = 90% or \(\frac{1}{10}\)
Total Income - Total Expenditure = Total Saving
Sum-up all expenditure, i.e \(\frac{18}{10} \times x = 5700 \Rightarrow x = \frac{5700 \times 10}{10} \Rightarrow x = 300 \Rightarrow 300 \times 29 = 8700\)
D
Lets take an example with the problem:
Income: 7, Expenditure: 20%, Saving: 100 - 20 = 80%. For simplicity, I'm considering expenditure here, i.e. 20% or \(\frac{2}{10}\)
Income: 4, Saving: 30%, Expenditure: 100 - 30 = 70 % or \(\frac{7}{10}\)
Income: 8, Saving 40%, Expenditure: 100-40 = 60% or \(\frac{6}{10}\)
Income: 10, Expenditure: 10%, Saving 100 - 10 = 90% or \(\frac{1}{10}\)
Total Income - Total Expenditure = Total Saving
Sum-up all expenditure, i.e \(\frac{18}{10} \times x = 5700 \Rightarrow x = \frac{5700 \times 10}{10} \Rightarrow x = 300 \Rightarrow 300 \times 29 = 8700\)
D
