Four friends, Priya, Kavya, Gaurvi and Shalini, have different amounts of money with them. If Priya takes ?88 from Kavya, then
she will have an amount equal to what Gaurvi has. Shalini and Kavya together have a total of Rs550. If Gaurvi takes Rs25 from
Shalini, she will have an amount equal to what Kavya has. If the total amount with Shalini, Kavya and Gaurvi is Rs840, how much
money does Priya have?
This questions was previously asked in
SSC CGL 20th August 2021 Shift-3
Explanation:
- Let's denote the amount of money each friend has: Priya as P, Kavya as K, Gaurvi as G, and Shalini as S.
- From the first statement: If Priya takes Rs88 from Kavya, Priya's amount will equal Gaurvi's. Thus, \(P + 88 = G\).
- The second statement: Shalini and Kavya together have Rs550. Thus, \(S + K = 550\).
- The third statement: If Gaurvi takes Rs25 from Shalini, Gaurvi's new total equals Kavya's amount. Thus, \(G + 25 = K\).
- Finally, the total amount with Shalini, Kavya, and Gaurvi is Rs840, so \(S + K + G = 840\).
By substituting these equations and solving them:
- Substitute \(G = P + 88\) in \(G + 25 = K\), then \(K = P + 88 + 25 = P + 113\).
- From \(S + K = 550\), we express Shalini as \(S = 550 - K\).
- Substituting \(K = P + 113\) into \(S + K + G = 840\), we get \(550 - K + K + P + 88 = 840\), simplifying to \(P = 202\).
- Therefore, Priya has Rs202.
- Answer: Option 4 - Rs202
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By: santosh