Arun divides Rs 4702 among A, B, and C, so that if the amounts being invested at 4% simple interest, the amounts received after 2, 3 and 4 yrs by A, B, and C respectively is equal. Find the share of B?a)Rs 1,458b)Rs 1,556c)Rs 2,358d)Rs 1,237e)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

B) Rs 1,556 Explanation: 4702 will be divided in ratio – 1/[100+rt1] : 1/[100+rt2] : 1/[100+rt3] 1/[100+4*2] : 1/[100+4*3] : 1/[100+4*4] 1/108 : 1/112 : 1/116
= 812 : 783 : 756
So B gets 783/(812+783+756) * 4702 = 1566

Answer

Given information:
- The total amount divided by Arun among A, B, and C is Rs 4702.
- The amounts invested by A, B, and C are given for 2, 3, and 4 years, respectively.
- The amounts received by A, B, and C after 2, 3, and 4 years, respectively, are equal.

Let's assume the amount invested by A, B, and C as x, y, and z, respectively.

Amount received by A after 2 years = x + (2 * x * 0.04) = x + (0.08x) = 1.08x
Amount received by B after 3 years = y + (3 * y * 0.04) = y + (0.12y) = 1.12y
Amount received by C after 4 years = z + (4 * z * 0.04) = z + (0.16z) = 1.16z

As per the given information, the amounts received by A, B, and C after 2, 3, and 4 years, respectively, are equal. Therefore, we can write the following equation:

1.08x = 1.12y = 1.16z

We know that x + y + z = Rs 4702.

To find the share of B, we need to calculate the value of y.

Calculation:
Let's solve the equation using the given information.

1.08x = 1.12y = 1.16z

From the equation, we can write:
1.08x = 1.12y
x/y = 1.12/1.08
x/y = 28/27

1.12y = 1.16z
y/z = 1.16/1.12
y/z = 29/28

We have the equation:
x/y = 28/27
y/z = 29/28

Let's solve these equations:

x/y = 28/27
Cross multiply:
27x = 28y
x = (28/27)y ----(1)

y/z = 29/28
Cross multiply:
28y = 29z
y = (29/28)z ----(2)

Substitute the value of y from equation (2) into equation (1):
x = (28/27)(29/28)z
x = (29/27)z

Now, substitute the values of x and y in the equation x + y + z = Rs 4702:
(29/27)z + (29/28)z + z = 4702
Multiplying through by 27 * 28:
(29 * 28 * z) + (29 * 27 * z) + (27 * 28 * z) = 4702 * 27 * 28

Simplifying:
(29(28z + 27z) + 27 * 28 * z) = 4702 * 27 * 28
(28z + 27z + 27z) = 4702
82z = 4702
z = 4702/82
z = 57.244

Therefore, the share of B (y) = (

Answer

B) Rs 1,556 Explanation: 4702 will be divided in ratio – 1/[100+rt1] : 1/[100+rt2] : 1/[100+rt3] 1/[100+4*2] : 1/[100+4*3] : 1/[100+4*4] 1/108 : 1/112 : 1/116
= 812 : 783 : 756
So B gets 783/(812+783+756) * 4702 = 1566

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