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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)
    8700
  • b)
    8500
  • c)
    8300
  • d)
    8900
  • e)
    7800
Correct answer is option 'A'. Can you explain this answer?
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Given:
The income of four persons are in the ratio of 7 : 4 : 8 : 10 respectively.

Calculating the Savings and Expenditure:
Let's assume the income of the four persons as 7x, 4x, 8x, and 10x respectively.

The first person spends 20% of his income, so the expenditure of the first person is 20% of 7x = (20/100) * 7x = 1.4x.

The second person saves 30% of his income, so the savings of the second person is 30% of 4x = (30/100) * 4x = 1.2x.

The third person saves 40% of his income, so the savings of the third person is 40% of 8x = (40/100) * 8x = 3.2x.

The fourth person spends 10% of his income, so the expenditure of the fourth person is 10% of 10x = (10/100) * 10x = 1x.

Calculating the Total Income and Total Expenditure:
The total income of the four persons is 7x + 4x + 8x + 10x = 29x.

The total expenditure of the four persons is 1.4x + 1.2x + 3.2x + 1x = 6.8x.

The difference between the total income and total expenditure is given as Rs 5700, so we have:

29x - 6.8x = 5700

Simplifying the equation:

22.2x = 5700

Dividing both sides by 22.2:

x = 5700 / 22.2 ≈ 256.76

Calculating the Total Income:
The total income of the four persons is 29x = 29 * 256.76 ≈ 7440.04.

Rounding off to the nearest whole number, the total income is approximately Rs 7440.

Conclusion:
The total income of all four persons is approximately Rs 7440, which is closest to option A) 8700.
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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)8700b)8500c)8300d)8900e)7800Correct answer is option 'A'. Can you explain this answer?
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