Question

Divide 4,864 into three parts such that the
second part is five times the first and the ratio
of the second part to the third part is 3: 4.​

Answer 1

Answer :-

384, 1920, 2560

Solution :-

No. given to divide = 4864

Ratio of second part to third part = 3 : 4

Let the common ratio be x

• Second part = 3x
• Third part = 4x

Given

Second part is 5 times times the first

⇒ First part is 1/5 times the Second pard

⇒ First part = 3x * 1/5 = 3x/5

We know that

Sum of all parts = 4864

⇒ 3x/5 + 3x + 4x = 4864

⇒ ( 3x + 15x + 20x ) / 5 = 4864

⇒ 38x / 5 = 4864

⇒ x = 4864 * 5 / 38

⇒ x = 640

First part = 3x/5 = 3 * 640 / 5 = 384

Second part = 3x = 3 * 640 = 1920

Third part = 4x = 4 * 640 = 2560

Therefore 4864 is divided into three parts 384, 1920, 2560.

Answer 2

${\mathtt{\orange{GIVEN}}}$

• We have to divide 4864 into 3 parts.
• 2nd part is 5 times 1st part
• Ratio of 2nd and 3rd part is 3:4

${\mathtt{\orange{Solution}}}$

$\mathtt{:⟹ \:Let\: the\:three\:parts\:as\:x\: , \:y \: ,\: z}$

$\mathtt{:⟹\: Now \: y \: = \: 5x \:\:\:\:\:\: as\: given}$

$\mathtt{:⟹\: And }$

$: ⟹ \: \frac{y}{z} = \frac{3}{4}$

$\mathtt{:⟹\: 4y \: = \: 3z}$

$:⟹ \: z = \frac{4}{3} y$

$: ⟹ \: z \: = \frac{4}{3} \times 5x$

$\mathtt{:⟹\:( y \: = \: 5x)}$

$\mathtt{:⟹ \: Now \: ratio\: of \: these \: three\: parts \: is }$

$: ⟹ \: x : y : z \: = x : 5x : \frac{20}{3} x$

$\mathtt{: ⟹ \: Multiplying\: by \: 3 }$

$\mathtt{:⟹\: 3x \: : 15x \: : 20x }$

$\mathtt{:⟹ \: 38x \: = \: 4864}$

$\mathtt{:⟹ \: 38x\: = \:38.(128)}$

$\mathtt{:⟹ \: x \:= \: 128 }$

$\mathtt{:⟹\: 1st \: part \:=\: 3(128)\: = \: 384}$

$\mathtt{:⟹\: 2nd\: part \: = \: 15(128) \: = \: 1920}$

$\mathtt{:⟹\: 3rd \: part \:= \: 20(128) \: = \: 2560}$

So the required numbers are 384 , 1920 and 2560 .