Question

Divide 2600 into three parts in such a way that the their interest on first part at the rate of 4%,on the second part at the rate 6%, and on the third part at the rate 8% is equal​

Answer 1

Answer:

Let the all three parts be a, b and c.

• Rate on a = 4%
• Rate on b = 6%
• Rate on c = 8%

Now here is a thing to understand, when Time isn't mentioned for interest. We can take any time for all of them and that will be cancelled inevitably, so let's take time as 1 year.

• According to the Question :

⇒ a × 4% × 1 = b × 6% × 1 = c × 8% × 1

• Cancelling Like terms i.e. % and 1 from all

⇒ a × 4 = b × 6 = c × 8

⇒ 4a = 6b = 8c

• Dividing each term by 2

⇒ 2a = 3b = 4c

• To bring on equal scale, we will multiply each of them by LCM(2, 3, 4) = 12

⇒ a/2 × 12 = b/3 × 12 = c/4 × 12

⇒ 6a = 4b = 3b

⇒ a : b : c = 6 : 4 : 3

Now we have ratio of each part, so we can find the exact figure. Let a, b and c be 6x, 4x and 3x

⠀⠀⠀⠀⠀───────────────

• Different parts will be as follow :

⇢ a + b + c = 2600

⇢ 6x + 4x + 3x = 2600

⇢ 13x = 2600

⇢ x = 2600/13

⇢ x = 200

• a = 6x = 6(200) = Rs. 1200
• b = 4x = 4(200) = Rs. 800
• c = 3x = 3(200) = Rs. 600

∴ Hence, all three parts are of Rs. 1200, Rs. 800 and Rs. 600 respectively.

Answer 2

${\boxed{\underline{\tt{ \orange{Required \: \: Answer:-}}}}}$

◉ GIVEN:-

• Total = 2600

• 1st interest = 4%

• 2nd interest = 6%

• 3rd interest = 8%

◉ TO FIND :-

• 1st interest

• 2nd interest

• 3rd interest

◉ SOLUTION:-

let the parts be x, y, and z.

• simple interest on x is 4% for 1 year.

• simple interest on y is 6% for 1 year.

• simple interest on z is 8% for 1 year.

$: \longrightarrow \frac{x \times 4 \times 1}{100} = \frac{y \times 6 \times 1}{100} = \frac{z \times 8 \times 1}{100}$

$: \longrightarrow \: 2x = 3y = 4z$

$: \longrightarrow \: x \ratio \: y \: = 3 \ratio1 = 6 \ratio4$

$: \longrightarrow \: x \ratio \: z = 2 \ratio1 = 6 \ratio3$

$: \longrightarrow \: x \: \ratio \: y \: \ratio \: z \: = 6 \ratio4 \ratio3$

$x = 2600 \times \frac{6}{6 + 4 + 3}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \leadsto \: { \boxed{ \underline{ \pink{x = 1200}}}}$

$y = 2600 \times \frac{4}{6 + 4 + 3}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \leadsto \: { \boxed{ \underline{ \pink{y =800 }}}}$

$z = 2600 \times \frac{3}{6 + 4 + 3}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \leadsto \: { \boxed{ \underline{ \pink{z = 600}}}}$

HOPE IT HELPS :)