Question

divide rupees 2040 among A,B and C such that A gets 2 by 3 of what B gets and B gets 1 by 4 of what C gets.​

Answer 1

Step-by-step explanation:

Let C gets ₹ x.

$\therefore$ B gets

$=\frac{1 } {4} \times C\\</p><p>=\frac{1 } {4} \:x$

$\&$ A gets

$=\frac{2}{3} \times B\\</p><p>=\frac{2}{3} \times\frac{1}{4} \:x\\ </p><p>=\frac{1} {6} \:x$

Now, it is given that:

A + B + C = 2040

$\therefore \frac{1}{6} \:x+\frac{1}{4} \:x+x = 2040\\\\</p><p>\therefore \frac {2x+3x+12x}{12}= 2040\\\\</p><p>\therefore \frac {17x}{12}= 2040\\</p><p>\therefore x = \frac {12} {17} \times 2040\\\\</p><p>\therefore x = 12\times 120\\\\</p><p>\huge\blue{ \boxed {\therefore x = 1440}} \\ \\</p><p>\implies \\</p><p>Share \: of \:A=\frac{1 } {6}\times x\\</p><p>=\frac{1}{6}\times 1440\\</p><p>\therefore\red{\boxed{Share \: of \:A= Rs.\: 240}}\\\\</p><p>Share \: of \:B=\frac{1} {4}\times x\\</p><p>=\frac{1} {4}\times 1440\\</p><p>\therefore\blue{\boxed{Share \: of \:B= Rs.\: 360}} \\\\\&\\</p><p>Share \: of \:C= x\\</p><p>\therefore\orange{\boxed{Share \: of \:C= Rs.\: 1440}}$

Verification:

240 + 360 + 1440 = 2040