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Question

A, B, C compare their fortunes :
A says to B, "give me ₹ 700 of your money, and I shall have twice as much as you retain".
B says to C, "give me ₹ 1400, and then I shall have thrice as much as you retain.'
C says to A, "give me ₹ 420, and then I shall have five times as much as you retain."
Find the fortunes of A, B and C.

A
A = ₹ 980, B = ₹ 1540, C = ₹ 2380
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B
A = ₹ 1583.44 , B = ₹ 1066.89, C = ₹ 2394.48
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C
A = ₹ 480, B = ₹ 2380, C = ₹ 1540
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D
A = ₹ 2396, B = ₹1583, C = ₹1067
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Solution

The correct option is A A = ₹ 980, B = ₹ 1540, C = ₹ 2380
Let A's fortune be ₹x, B's fortune be ₹y and C's fortune be ₹z.

x+700=2(y700)x+700=2y1400x2y=2100.....(1)

y+1400=3(z1400)y+1400=3z4200y3z=5600.....(2)

z+420=5(x420)z+420=5x2100z5x=2520.....(3)

eqn(2)+eqn(3)×3y3z=560015y+3z=7560
__________________
y15x=13160.............(4)

eqn(1)+eqn(4)×2x2y=210030x+2y=26320
__________________
29x=26320x=980.............(5)

Substituting eqn(5) in eqn(1), we get,
9802y=21002y=3080y=1540...........(6)

Substituting eqn(6) in eqn(2), we get,
15403z=56003z=7140z=2380...........(7)

A's fortune = ₹ 980
B's fortune = ₹ 1540
C's fortune = ₹ 2380

Verification:
A's fortune + ₹ 700 = ₹ 980 + 700
= ₹1680

B's fortune - ₹ 700 = ₹ 1540 - 700
= ₹840

Clearly, 1680 = 2(840)

B's fortune + ₹ 1400 = ₹1540 + ₹1400
= ₹2940

C's fortune - ₹ 1400 = ₹2380 - ₹1400
= ₹980

Clearly, 2940 = 3(980)

A's fortune - ₹ 420 = ₹ 980 - 420
= ₹560

C's fortune + ₹420 = ₹2380 + ₹420
= ₹2800

Clearly, 2800 = 5(560)

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