Four friends Ashok, Bashir, Chirag and Deepak are out shopping. Ashok has less money than three times the amount that Bashir has. Chirag has more money than Bashir. Deepak has an amount equal to the difference of amounts with Bashir and Chirag. Ashok has three times the money with Deepak. 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. Chirag borrows Rs. 300 from Ashok and buys a jacket. Bashir buys a sweater after borrowing Rs. 100 from Ashok and is left with no money. Ashok buys three shirts. What is the costliest item the Deepak could buy with his own money?
Explanation:
Let Ashok, Bashir, Chirag and Deepak have amounts Rs. A, Rs. B, Rs. C and Rs. D respectively. From the data given in the question, we have following equations.
A < 3B ... (i)
C > B ... (ii)
D = C − B ... (iii)
A = 3D ... (iv)
Chirag borrows Rs. 300 from Ashok and buys a jacket worth Rs. 1000.
∴ C ≥ 700 ... (v)
Bashir buys a sweater after borrowing Rs. 100 from Ashok and left with no money.
∴ B = 500 ... (vi)
Ashok buys 3 shirts (costing Rs. 600 in total) with Rs. A − 300 − 100
∴ A ≥ 1000
From (i) and (vi), we get,
A < 1500
∴ 1000 ≤ A < 1500 ... (vii)
From equation (iv) and (vii), we get,
333 < D < 500
∴ Deepak could buy a shawl worth Rs. 400.
Hence, option (b).
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