Question 36. Four friends Atul, Balraj, Chaitanya and Dharmendra are out for sports shopping. Atul has less money than three times the amount that Balraj has. Chaitanya has more money than Balraj. Dharmendra has an amount equal to the difference of amounts with Balraj and Chaitanya. Atul has three times the money with Dharmendra. They each have to buy at least one hockey, or one cricket bat, or baseball set, or football kit that are priced Rs. 200, Rs.400, Rs. 600, and Rs. 1000 a piece, respectively. Chaitanya borrows Rs. 300 from Atul and buys a football kit. Balraj buys a baseball set after borrowing Rs.100 from Atul and is left with no money. Atul buys three hockey. What is the costliest item the Dharmendra could buy with his own money?

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Mukul has three times as much as Atul. If Mukul gives Rs. 250 to Atul, Atul will have twice as much Mukul. How much did each of them have?

letamountMukulhas=xandthatofAtul=yx=3y→(1.)2×(x−250)=(y+250)2x−500=y+2502(3y)−y=7505y=750∴y=150Rs∴x=3y=450Rs

Mukul has three times as much as Atul. If Mukul gives Rs. $250$ to Atul, Atul will have twice as much Mukul. How much did each of them have?

$l e t a m o u n t M u k u l h a s = x a n d t h a t o f A t u l = y x = 3 y \to (1.) 2 \times (x - 250) = (y + 250) 2 x - 500 = y + 250 2 (3 y) - y = 750 5 y = 750 ∴ y = 150 R s ∴ x = 3 y = 450 R s$