The Spendthrifts
Four friends Asha, Babu, Chika and Dishant are out for shopping. Asha has less money than three times the amount that Babu has. Chika has more money than Babu. Dishant has an amount equal to the difference of amounts with Babu and Chika. Asha has three times the money with Dishant. They each have to buy at least one shirt, or one shawl, or one sweater, or one jacket that are priced Rs. 200, Rs. 400, Rs. 600, and Rs. 1,000 a piece respectively.
- Chika borrows Rs. 300 from Asha and buys a jacket.
- Babu buys a sweater after borrowing Rs. 100 from Asha and is left with no money.
- Asha buys three shirts.
Which is the costliest item that Dishant could buy with his own money?
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1 solution
"Asha has less money than three times the amount that Babu has. Chika has more money than Babu. Dishant has an amount equal to the difference of amounts with Babu and Chika. Asha has three times the money with Dishant."
A < 3B
C > B
D = C - B
A = 3D
Babu buys a sweater after borrowing Rs. 100 from Asha and is left with no money. b = B + 100 - 600 { price of sweater } = 0
B = 500
A < 3(500) = 1500
C > 500
Chika borrows Rs. 300 from Asha and buys a jacket.
500 < C < 1000 { price of jacket }
c < 1000 + 300 - 1000 = 300
Asha buys three shirts.
a < 1500 - 100 - 300 - 3(200) { price of shirt }
a < 500
D = C - B
D < 1000 - 500
D < 500
Maximizing, D = 499 > 400 { price of one shawl }