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Four young men and fast friends – Anirban, Bhaskar, Shubhayu and Sugato, who had been placed in top companies at their hometown Kolkata directly from college in 2021, decided to splurge their 2022 Durga Puja bonus payments on themselves. They went shopping together and each purchased at least one out of the three items -- an iPhone-14, a Bose Music System and an LG Microwave Oven.
The costs of these three items were Rs 78,750, Rs 33,750 and Rs 45,000, in no particular order.
It was also known that :
a) No friend purchased more than one item of any type.
b) Also, it was known that one of the friends did not purchase an iPhone-14, one of them did not purchase the Bose Music System, and two of them did not purchase the LG Microwave Oven.
c) Anirban spent the most and Shubhayu spent the least.
d) No two friends spent the same amount.
Question:- If Shubhayu spent Rs 33,750 and Sugato spent the second highest amount among the four friends, then what could be the minimum amount that Bhaskar had spent ?
Rs 123750
Rs 112500
Rs 78750
Rs 45000
From the explanations provided in the first question, we know that when the cost of the LG Microwave Oven was not Rs 78,750, four different situations arose, as is again given below :
1 A) If the iPhone 14 costs Rs 78750, the LG Microwave Oven costs Rs 33750 and the Bose Music System costs Rs 45000, then the expenses were :
Case 1A |
iPhone 14 |
Bose Music System |
LG Microwave Oven |
Total Expense |
Anirban |
Yes |
Yes |
Yes |
(78750+45000+33750) = Rs 157500 |
Bhaskar/Sugato |
Yes |
No |
Yes |
(78750+33750) = Rs 112500 |
Shubhayu |
No |
Yes |
No |
Rs 45000 |
Sugato/Bhaskar |
Yes |
Yes |
No |
(78750+45000) = Rs 123750 |
1 B) If the iPhone 14 costs Rs 78750, the LG Microwave Oven costs Rs 45000 and the Bose Music System costs Rs 33750, then the expenses were :
Case 1B |
iPhone 14 |
Bose Music System |
LG Microwave Oven |
Total Expense |
Anirban |
Yes |
Yes |
Yes |
(78750+33750+45000) = Rs 157500 |
Bhaskar/Sugato |
Yes |
No |
Yes |
(78750+45000) = Rs 123750 |
Shubhayu |
No |
Yes |
No |
Rs 33750 |
Sugato/Bhaskar |
Yes |
Yes |
No |
(78750+33750) = Rs 112500 |
2 A) If the Bose Music System costs Rs 78750, the LG Microwave Television costs Rs 33750 and the iPhone 14 costs Rs 45000, then the expenses were :
Case 2A |
iPhone 14 |
Bose Music System |
LG Microwave Oven |
Total Expense |
Anirban |
Yes |
Yes |
Yes |
(45000+78750+33750) = Rs 157500 |
Bhaskar/Sugato |
No |
Yes |
Yes |
(78750+33750) = Rs 112500 |
Shubhayu |
Yes |
No |
No |
Rs 45000 |
Sugato/Bhaskar |
Yes |
Yes |
No |
(45000+78750) = Rs 123750 |
2 B) If the Bose Music System costs Rs 78750, the LG Microwave Television costs Rs 45000 and the iPhone 14 costs Rs 33750, then the expenses were :
Case 2B |
iPhone 14 |
Bose Music System |
LG Microwave Oven |
Total Expense |
Anirban |
Yes |
Yes |
Yes |
(33750+78750+45000) = Rs 157500 |
Bhaskar/Sugato |
No |
Yes |
Yes |
(78750+45000) = Rs 123750 |
Shubhayu |
Yes |
No |
No |
Rs 33750 |
Sugato/Bhaskar |
Yes |
Yes |
No |
(33750+78750) = Rs 112500 |
It can be seen that only in Case 1B and Case 2B Shubhayu spent Rs 33750.
Sugato spent the second highest amount among the four friends, which in Case 1B and Case 2B was Rs 123750.
Hence in Case 1B and Case 2B Bhaskar spent Rs 112500.
But we also need to consider the remaining case where cost of the LG Microwave Oven was Rs 78,750.
It gives rise to four different cases 1C, 1D, 2C and 2D.
1 C) If the LG Microwave Oven costs Rs 78750, the iPhone 14 costs Rs 33750 and the Bose Music System costs Rs 45000, then the expenses were :
Case 1C |
iPhone 14 |
Bose Music System |
LG Microwave Oven |
Total Expense |
Anirban |
Yes |
Yes |
Yes |
(33750+45000+78750)= Rs 157500 |
Bhaskar/Sugato |
Yes |
No |
Yes |
(33750+78750) = Rs 112500 |
Shubhayu |
No |
Yes |
No |
Rs 45000 |
Sugato/Bhaskar |
Yes |
Yes |
No |
(33750+45000) = Rs 78750 |
1 D) If the LG Microwave Oven costs Rs 78750, the iPhone 14 costs Rs 45000 and the Bose Music System costs Rs 33750, then the expenses were :
Case 1D |
iPhone 14 |
Bose Music System |
LG Microwave Oven |
Total Expense |
Anirban |
Yes |
Yes |
Yes |
(45000+33750+78750)= Rs 157500 |
Bhaskar/Sugato |
Yes |
No |
Yes |
(45000+78750) = Rs 123750 |
Shubhayu |
No |
Yes |
No |
Rs 33750 |
Sugato/Bhaskar |
Yes |
Yes |
No |
(45000+33750) = Rs 78570 |
2 C) If the LG Microwave Oven costs Rs 78750, the iPhone 14 costs Rs 33750 and the Bose Music System costs Rs 45000, then the expenses were :
Case 2C |
iPhone 14 |
Bose Music System |
LG Microwave Oven |
Total Expense |
Anirban |
Yes |
Yes |
Yes |
(33750+45000+78750)= Rs 157500 |
Bhaskar/Sugato |
No |
Yes |
Yes |
(45000+78750) = Rs 123750 |
Shubhayu |
Yes |
No |
No |
Rs 33750 |
Sugato/Bhaskar |
Yes |
Yes |
No |
(33750+45000) = Rs 78570 |
2 D) If the LG Microwave Oven costs Rs 78750, the iPhone 14 costs Rs 45000 and the Bose Music System costs Rs 33750, then the expenses were :
Case 2D |
iPhone 14 |
Bose Music System |
LG Microwave Oven |
Total Expense |
Anirban |
Yes |
Yes |
Yes |
(45000+33750+78750)= Rs 157500 |
Bhaskar/Sugato |
No |
Yes |
Yes |
(33750+78750) = Rs 112500 |
Shubhayu |
Yes |
No |
No |
Rs 45000 |
Sugato/Bhaskar |
Yes |
Yes |
No |
(45000+33750) = Rs 78750 |
It can be seen that only in Case 1D and Case 2D Shubhayu spent Rs 33750.
Sugato spent the second highest amount among the four friends, which in Case 1D was Rs 123750 and in Case 2D was Rs 112500.
Hence in Case 1D and Case 2D Bhaskar spent Rs 78750.
Hence, if Shubhayu spent Rs 33,750 and Sugato spent the second highest amount among the four friends, then the minimum amount that Bhaskar had spent was Rs 78750.