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The ratio of income of A and B is 2:3. The sum of their expenditure is Rs.8000 and the amount of savings of A is equal to the amount of expenditure of B.What is the their ratio of  sum of income to their sum of savings?
  • a)
    5:3
  • b)
    3:2
  • c)
    4:3
  • d)
    3:1
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?
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The ratio of income of A and B is 2:3. The sum of their expenditure is...
Answer -A.5:3 Explanation : 2I-E + E = 8000
I = 4000
Sum of their Income = 5*I = 5*4000 = 20,000 Sum of their Savings = 20000-8000 = 12,000 20000:12000 = 5:3
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The ratio of income of A and B is 2:3. The sum of their expenditure is...
Answer -A.5:3 Explanation : 2I-E + E = 8000
I = 4000
Sum of their Income = 5*I = 5*4000 = 20,000 Sum of their Savings = 20000-8000 = 12,000 20000:12000 = 5:3
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The ratio of income of A and B is 2:3. The sum of their expenditure is...
Given:
- Income ratio of A and B is 2:3
- Sum of their expenditure is Rs.8000
- Savings of A is equal to expenditure of B

To find:
- Ratio of sum of income to sum of savings

Solution:
Let the income of A and B be 2x and 3x respectively.

Since the savings of A is equal to the expenditure of B,
Savings of A = Expenditure of B
=> Income of A - Expenditure of A = Expenditure of B
=> 2x - (8000 - Expenditure of B) = Expenditure of B
=> 3x = Expenditure of B + 8000

Adding the expenditure of A and B, we get:
Expenditure of A + Expenditure of B = 8000
=> Expenditure of A + (3x - 8000) = 8000
=> Expenditure of A = 16000 - 3x

Savings of A = Expenditure of B
=> Savings of A = 8000 - Expenditure of A
=> 2x = 8000 - (16000 - 3x)
=> 5x = 8000
=> x = 1600

Therefore, the income of A and B are 2x and 3x respectively, which is 3200 and 4800.

Sum of income = 3200 + 4800 = 8000
Sum of savings = Savings of A + Savings of B = Expenditure of B + Expenditure of A = 8000

Ratio of sum of income to sum of savings = 8000/8000 = 1

Hence, the ratio of sum of income to sum of savings is 5:3 (Option A).
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The ratio of income of A and B is 2:3. The sum of their expenditure is Rs.8000 and the amount of savings of A is equal to the amount of expenditure of B.What is the their ratio of sum of income to their sum of savings?a)5:3b)3:2c)4:3d)3:1e)None of theseCorrect answer is option 'A'. Can you explain this answer?
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