Question

66. ₹x is divided among A, B, and C. The share of A is two-fifth of the total money, the share of B is two third of the remaining money, and the share of C is ₹600. Find the value of x.
Options:

1.3000
2.4000
3.5000
4.6000



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Answer 1

$\bf{WE \: \: KNOW \: THAT}$

$\sf{The \: Total \: \: money =x \: ₹}$

$\small \text{The share of A is two-fifth of the total money} \\\\ = A = ₹ \: \frac{2}{5} \: \sf{x}$

$\small \text{The share of B is two third of the remaining money} \\\\ B= \frac{2}{3} \sf{(₹ \: x - ₹ \: \frac{2x}{5} )} = \frac{2x}{5}$

$\small \text{The share of C is ₹600 } \\\\C = ₹600$

$\bf{THEREFORE}$

$\sf{ \frac{2x}{5} + \frac{2x}{5} + 600 = x}$

$\sf{> > x - \frac{4x}{5} = 600} \\\\ \sf{> > \frac{x}{5} = 600}$

$\bf{x = 600 \: ( 5)}$

$\bf{> > x = 3000}$

$\bf \huge \purple{Hence}$

$\small \text{The value of x \: is \: 3000.}$

$\bf{Option \: one \: (1) \: is \: correct}$

Answer 2

$\huge\color{purple}{ \colorbox{orange}{\colorbox{white} {Answer}}}$

total money is : Rs x

Given,

• The share of A

$= Rs \: \frac{2}{5} x$

• The share of B

$= \frac{2}{3} (Rs \: x - Rs\: \frac{2x}{5} ) = Rs\frac{2x}{5}$

• The share of C

$= Rs \: 600$

$∴\frac{2}{5} x \: + \frac{2x}{5} \: + 600 = x$

$x = \frac{4x}{5} = 600→ \frac{x}{5} = 600$

$= 600(5)$

$= 3000$

Total money = 3000

hence, option (1) is correct