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If Radha saves 25% of her income, if the...

If Radha saves 25% of her income, if the expenditure is increased by 20% and income is increased by 29%. Find change% in saving.

A

` 48 % `

B

` 56 % `

C

` 52 % `

D

` 60 % `

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to determine the change in Radha's savings after her income and expenditure have both changed. Let's break it down step by step. ### Step 1: Define Radha's Initial Income and Expenditure Let Radha's initial income be \( I \). Since Radha saves 25% of her income, her savings \( S \) can be calculated as: \[ S = 0.25I \] This means her expenditure \( E \) is: \[ E = I - S = I - 0.25I = 0.75I \] ### Step 2: Calculate the New Income Radha's income increases by 29%. Therefore, her new income \( I' \) is: \[ I' = I + 0.29I = 1.29I \] ### Step 3: Calculate the New Expenditure Her expenditure increases by 20%. The new expenditure \( E' \) is: \[ E' = E + 0.20E = 1.20E = 1.20 \times 0.75I = 0.90I \] ### Step 4: Calculate the New Savings Now we can calculate Radha's new savings \( S' \): \[ S' = I' - E' = 1.29I - 0.90I = 0.39I \] ### Step 5: Calculate the Change in Savings The change in savings can be calculated as: \[ \text{Change in Savings} = S' - S = 0.39I - 0.25I = 0.14I \] ### Step 6: Calculate the Percentage Change in Savings To find the percentage change in savings, we use the formula: \[ \text{Percentage Change} = \left(\frac{\text{Change in Savings}}{\text{Initial Savings}}\right) \times 100 \] Substituting the values we found: \[ \text{Percentage Change} = \left(\frac{0.14I}{0.25I}\right) \times 100 = \left(\frac{0.14}{0.25}\right) \times 100 = 56\% \] ### Final Answer The percentage change in Radha's savings is **56%**. ---
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