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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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A sum of ₹6,820 is divided between Vikas, Tina and Sumit such that if their shares are decreased by ₹470, ₹110 and ₹540, respectively, then they are in the ratio of 4 : 9 : 7. What is the original share of Tina?
₹2,675
₹2,745
₹2,760
₹2,479
₹2,675
Shortcut Trick Total reduction = 470 + 110 + 540 = 1120 Remaining sum = 6820 − 1120 = 5700 Total ratio parts = 4 + 9 + 7 = 20 units 1 unit = 5700 ÷ 20 = 285 Tina's share = (9 units × 285) + 110 = 2565 + 110 = 2675 ∴ The correct answer is ₹2,675. A...
Shortcut Trick
Total reduction = 470 + 110 + 540 = 1120
Remaining sum = 6820 − 1120 = 5700
Total ratio parts = 4 + 9 + 7 = 20 units
1 unit = 5700 ÷ 20 = 285
Tina's share = (9 units × 285) + 110 = 2565 + 110 = 2675
∴ The correct answer is ₹2,675.
Alternate Method
Given:
Total sum = ₹6,820
Decrements: Vikas = ₹470, Tina = ₹110, Sumit = ₹540
Ratio after decrement = 4 : 9 : 7
Formula:
Total Effective Sum = Sum of all ratio parts × Constant unit value
⇒ Total reduced sum = 6820 − (470 + 110 + 540)
⇒ Total reduced sum = 6820 − 1120 = ₹5,700
⇒ Ratio sum = 4 + 9 + 7 = 20 units
⇒ 20 units = 5700
⇒ 1 unit = 5700 ÷ 20 = 285
⇒ Tina's share (after decrement) = 9 × 285 = ₹2,565
⇒ Tina's original share = 2565 + 110 = ₹2,675
∴ The correct answer is ₹2,675.
Additional Information
Ratio of Shares
If a sum S is divided into three parts in the ratio a : b : c, then the second part is calculated as [b / (a + b + c)] × S.
Effective Sum Method
When shares are decreased or increased by specific values, always calculate the new total sum first before applying the ratio parts.
Proportion Rule
If a : b = c : d, then a × d = b × c. This is the product of extremes equals the product of means.