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

Answer 1

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.

$x+700=2(y-700)x+700=2y-1400x-2y=-2100.....\left(1\right)$

$y+1400=3(z-1400)y+1400=3z-4200y-3z=-\mathrm{5600.....}\left(2\right)$

$z+420=5(x-420)z+420=5x-2100z-5x=-2520.....\left(3\right)$

$eqn\left(2\right)+eqn\left(3\right)\times 3y-3z=-5600-15y+3z=-7560$
__________________
$y-15x=-13160.............\left(4\right)$

$eqn\left(1\right)+eqn\left(4\right)\times 2x-2y=-2100-30x+2y=-26320$
__________________
$-29x=-26320x=₹980.............\left(5\right)$

Substituting eqn(5) in eqn(1), we get,
$980-2y=-21002y=3080y=₹\mathrm{1540...........}\left(6\right)$

Substituting eqn(6) in eqn(2), we get,
$1540-3z=-56003z=7140z=₹\mathrm{2380...........}\left(7\right)$

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)