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Two friends Seema and Rekha went to shop...

Two friends Seema and Rekha went to shopping with equal amount of money. Seema bought a shoe for Rs 95 and Rekha spent Rs 350 on dresses. If Rekha had 4/7 of what Seema had left. How much money did Seema have left after shopping?
(a)Rs 595
(b)Rs 690
(c)Rs 535
(d)Rs 495

A

Rs 595

B

Rs 690

C

Rs 535

D

Rs 495

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we can follow these calculations: 1. **Define the Initial Amount**: Let the amount of money that both Seema and Rekha initially had be \( X \). 2. **Calculate the Amount Left for Seema**: Seema spent Rs 95 on shoes. Therefore, the amount of money left with Seema after her purchase is: \[ \text{Seema's remaining amount} = X - 95 \] 3. **Calculate the Amount Left for Rekha**: Rekha spent Rs 350 on dresses. Therefore, the amount of money left with Rekha after her purchase is: \[ \text{Rekha's remaining amount} = X - 350 \] 4. **Set Up the Equation**: According to the problem, Rekha has \( \frac{4}{7} \) of what Seema has left. This gives us the equation: \[ X - 350 = \frac{4}{7}(X - 95) \] 5. **Clear the Fraction**: To eliminate the fraction, multiply both sides of the equation by 7: \[ 7(X - 350) = 4(X - 95) \] 6. **Expand Both Sides**: Expanding both sides of the equation: \[ 7X - 2450 = 4X - 380 \] 7. **Rearrange the Equation**: Move all terms involving \( X \) to one side and constant terms to the other side: \[ 7X - 4X = 2450 - 380 \] Simplifying this gives: \[ 3X = 2070 \] 8. **Solve for \( X \)**: Divide both sides by 3 to find \( X \): \[ X = \frac{2070}{3} = 690 \] 9. **Calculate Seema's Remaining Amount**: Now that we know \( X \), we can find out how much money Seema has left: \[ \text{Seema's remaining amount} = 690 - 95 = 595 \] Thus, the amount of money Seema has left after shopping is **Rs 595**. ### Final Answer: (a) Rs 595
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