Rajesh has Rs. 850 in his purse made up entirely of notes of Rs. 50…
2024
Rajesh has Rs. 850 in his purse made up entirely of notes of Rs. 50 denomination. His wife Latha, on the other hand, has only notes of Rs. 20 denomination in her purse and they amount to Rs. 460. Rajesh and Latha redistribute the notes between the two purses so that if one were to choose one of the two purses at random and then randomly draw a note from it, the probability of the note being of Rs. 50 denomination is maximized. After this redistribution, there will be a total of Rs. in the purse with the larger amount of money.
- A.
650 Rs
- B.
670 Rs
- C.
1260 Rs
- D.
720 Rs
Attempted by 228 students.
Show answer & explanation
Correct answer: C
Key idea: To maximize the probability of drawing a Rs.50 note, put exactly one Rs.50 note alone in one purse so that selecting that purse guarantees a Rs.50 note; place all remaining notes in the other purse.
Step 1 — Count the notes: 850/50 = 17 fifty-rupee notes; 460/20 = 23 twenty-rupee notes.
Step 2 — Redistribute: Put 1 fifty-rupee note alone in one purse. The other purse gets the remaining 16 fifty-rupee notes and all 23 twenty-rupee notes.
Step 3 — Compute the probability: If a purse is chosen at random (probability 1/2 each), probability of a Rs.50 note = 1/2×1 (from the single-note purse) + 1/2×(16/39) (from the other purse with 16 fifty-rupee notes out of 39 total notes) = 1/2 + 1/2×16/39 ≈ 0.705.
Step 4 — Compute amounts: The single-note purse has Rs.50. The other purse has 16×50 + 23×20 = 800 + 460 = Rs.1260.
Therefore, after the optimal redistribution, the purse with the larger amount contains Rs.1260.