A-certain-amount-of-money-is-distributed-among-A-B-and-C-in-the-ratio-of-2-5-3-and-another-amount-of-money-among-B-D-and-E-is-also-distributed-in-the-same-ratio-If-the-amount-distributed-among-A-

Question Number 176215 by MathsFan last updated on 15/Sep/22

A certain amount of money is distributed among A, B and C in the ratio of 2:5:3 and another amount of money among B, D and E is also distributed in the same ratio. If the amount distributed among A, B and C is ⅖ of the amount distributed among B, D and E, what is the ratio in which the amount is distributed among A, C and E?

Answered by Rasheed.Sindhi last updated on 15/Sep/22

Let the amount distributed among B,D & E is x. B receives ((2x)/(2+5+3))=(x/5) D ((5x)/(2+5+3))=(x/2) E ((3x)/(2+5+3))=((3x)/(10)) Amount distributed among A,B & C is then (2/5)x A receives ((2((2/5)x))/(2+5+3))=((4x)/(5×10))=((2x)/(25)) B ((5((2/5)x))/(2+5+3))=(x/5) C ((3((2/5)x))/(2+5+3))=((6x)/(5×10))=((3x)/(25)) determinant ((A,:,C,:,E),(((2x)/(25)),:,((3x)/(25)),:,((3x)/(10))),((((50)/x)×((2x)/(25))),:,(((50)/x)×((3x)/(25))),:,(((50)/x)×((3x)/(10)))),(4,:,6,:,(15)))

L e t t h e a m o u n t d i s t r i b u t e d a m o n g

B, D & E i s x .

B r e c e i v e s \frac{2 x}{2 + 5 + 3} = \frac{x}{5}

D \frac{5 x}{2 + 5 + 3} = \frac{x}{2}

E \frac{3 x}{2 + 5 + 3} = \frac{3 x}{10}

A m o u n t d i s t r i b u t e d a m o n g A, B &

C i s t h e n (2 / 5) x

A r e c e i v e s \frac{2 (\frac{2}{5} x)}{2 + 5 + 3} = \frac{4 x}{5 \times 10} = \frac{2 x}{25}

B \frac{5 (\frac{2}{5} x)}{2 + 5 + 3} = \frac{x}{5}

C \frac{3 (\frac{2}{5} x)}{2 + 5 + 3} = \frac{6 x}{5 \times 10} = \frac{3 x}{25}

\begin{array}{cccc} A & : & C & : & E \\ \frac{2 x}{25} & : & \frac{3 x}{25} & : & \frac{3 x}{10} \\ \frac{50}{x} \times \frac{2 x}{25} & : & \frac{50}{x} \times \frac{3 x}{25} & : & \frac{50}{x} \times \frac{3 x}{10} \\ 4 & : & 6 & : & 15 \end{array}

Commented by MathsFan last updated on 15/Sep/22

but sir, how did you get ((50)/x) in the table

but sir, how did you get \frac{50}{x} in the table

Commented by Rasheed.Sindhi last updated on 16/Sep/22

Simplifying ((2x)/(25)):((3x)/(25)):((3x)/(10)) (i) Multiply by LCM(25,10)=50_((to get rid of denominator)) 4x:6x:15x (ii)Now divide by common factor x 4:6:15 The two steps at a time, multiply by ((50)/x)

S i m p l i f y i n g \frac{2 x}{25} : \frac{3 x}{25} : \frac{3 x}{10}

(i) \underset{(t o g e t r i d o f d e n o m i n a t o r)}{M u l t i p l y b y LCM (25, 10) = 50}

4 x : 6 x : 15 x

(i i) N o w d i v i d e b y c o m m o n f a c t o r x

4 : 6 : 15

T h e t w o s t e p s a t a t i m e, m u l t i p l y b y

\frac{50}{x}

Commented by Tawa11 last updated on 18/Sep/22

Great sir

Answered by Rasheed.Sindhi last updated on 15/Sep/22

determinant ((A,B,C,D,E),(,2,,5,3),(2,5,3,,),(4,(10),6,(25),(15)),(4,,6,,(15)))

\begin{array}{ccccc} A & B & C & D & E \\ 2 & 5 & 3 \\ 2 & 5 & 3 \\ 4 & 10 & 6 & 25 & 15 \\ 4 & 6 & 15 \end{array}

Commented by MathsFan last updated on 15/Sep/22

thank you very much sir

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