Question

a sum of ₹7000 is divided among a, B, C, in such a way that the shares of a and B are in the ratio 2:3 and those of b and c are in the ratio 4:5. find the number.

Answer 1

$\textbf{Answer}$

Total money = Rs 7000

$\textbf{Share of A and B = 2 : 3}$

Suppose,
Share of A is 2x ----------(1)

=> Share of B = 3x -------(2)


We are also given that,

$\textbf{Share of B and C = 4 : 5}$

Above ratio means, if B gets 4 parts,then C gets 5 parts.
So if B gets 3x parts,
Share of C = (5/4)(3x)

Share of C = (15x/4) -------(3)


Since total sum = 7000
By using statements (1), (2) & (3),

2x + 3x + (15x/4) = 7000

=> 5x + 15x/4 = 7000

=> (20x + 15x) = 4 × 7000

=> 35x = 28000

=> x = 28000/35

=> x = 800

=> $\textbf{Share of A = 2x = Rs 1600}$
=> $\textbf{Share of B = 3x = Rs 2400}$
=> $\textbf{Share of C = 15x/4 = Rs 3000}$


$\textbf{Hope It Helps}$

$\textbf{Thanks}$

Answer 2

To make the sum of money of B same in both, taking LCM,

LCM = 12

So,

$\frac{a}{b} = \frac{2}{3} = \frac{2 \times 4}{ 3\times 4} = \frac{8}{12} \\ \frac{b}{c} = \frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}$

Now, sum of money of b is same in both,

Let, sum of money of :

a = 8x ; b = 12x ; c = 15x

Their sum = 7000

→ 8x + 12x + 15x = 7000

→ 35x = 7000

→ x = 200

Hence,

Money of a = 8x = 8(200) = ₹1600

Money of b = 12x = 12(200) =₹ 2400

Money of c = 25x = 15(200) = ₹3000