Question

Divide 13680 in three parts such that 1st part is 3/5th of the third part and the ratio between 2nd and 3rd part is 4:7.How much is the first part?

Answer 1

third part is 7x and 2nd part is 4x

first part will be 7x×3/5= 21x/5

now (21x+35x+20x)÷5 = 13680

76x = 13680×5

x= 900

first part is 900×21x/5= 3780

Answer 2

The first part is 3780.

Step-by-step explanation:

Let us assume that the three parts are x, y, and z.

So, x + y + z = 13680 .......... (1)

Given that, 1st part is $\frac{3}{5}$ th of the third part and the ratio between the 2nd and 3rd part is 4:7.

So that,  $x = \frac{3}{5}z$ and $\frac{y}{z} = \frac{4}{7}$, ⇒ $y = \frac{4}{7}z$

Therefore, from equation (1) we can write

$\frac{3}{5}z + \frac{4}{7}z + z = 13680$

⇒ $z(\frac{3 \times 7 + 4 \times 5 + 35}{35}) = 13680$

⇒ $\frac{76z}{35} = 13680$

⇒ z = 6300

Hence, $x = \frac{3}{5}z = 3780$

Therefore, the first part is 3780. (Answer)