P and Q entered into a partnership with initial investments of Rs. Y and Rs. Z respectively. After 18 months they both added some amount to their initial investments such that the investmentof P for the rest ofperiod is twice that of Qafter added. Profit share of P is 17220 out of total profit of Rs. 28290 after three years. If Z is 50% more than that of Y, find by what % ofQ increased his investment after 18 months?a)200%b)50%c)100%d)400%e)None of theseCorrect answer is option 'C'. Can you explain this answer?

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P and Q entered into a partnership with initial investments of Rs. Y and Rs. Z respectively. After 18 months they both added some amount to their initial investments such that the investmentof P for the rest ofperiod is twice that of Qafter added. Profit share of P is 17220 out of total profit of Rs. 28290 after three years. If Z is 50% more than that of Y, find by what % ofQ increased his investment after 18 months?

a)
200%
b)
50%
c)
100%
d)
400%
e)
None of these

Correct answer is option 'C'. Can you explain this answer?

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P and Q entered into a partnership with initial investments of Rs. Y ...

Let initial investment of P = 2a

So, initial investment of Q = 3a

Let investment of Q after 18 months = b

So, investment of P after 18 months = 2 x b = 2b

Now,

Ratio of profit share of P and Q = (2a x 1 + 2b x 1): (3a x 1 + b x 1) = (2a + 2b): (3a + b)

(2a + 2b)/ (2a + 2b + 3a + b) = 17220/28290

(2a + 2b) / (5a + 3b) = 14/23

23a + 23b = 35a + 21b

2b = 12a

So, value of b = 6a

Required % change = (6a – 3a)/3a x 100 = 100%

Hence, answer is option C

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P and Q entered into a partnership with initial investments of Rs. Y ...

Given Information:
- Initial investments of P and Q are Rs. Y and Rs. Z respectively.
- After 18 months, both P and Q added some amount to their initial investments.
- The investment of P for the rest of the period is twice that of Q after the addition.
- Profit share of P is Rs. 17220 out of the total profit of Rs. 28290 after three years.
- Z is 50% more than Y.

To find: By what percentage did Q increase his investment after 18 months?

Let's solve this step by step:

Step 1: Calculate the initial investments of P and Q
- Given that Z is 50% more than Y, we can write Z = Y + (50/100)Y = 1.5Y
- Therefore, the initial investments are Y and 1.5Y for P and Q respectively.

Step 2: Calculate the profit share of P and Q
- The profit share of P is Rs. 17220 out of the total profit of Rs. 28290.
- This means the profit share of Q is Rs. 28290 - Rs. 17220 = Rs. 11070.

Step 3: Calculate the ratio of investments after 18 months
- Let the additional amount invested by P and Q after 18 months be A and B respectively.
- According to the given condition, the investment of P for the rest of the period is twice that of Q.
- Therefore, (Y + A) / (1.5Y + B) = 2.

Step 4: Calculate the values of A and B
- Multiply both sides of the equation by (1.5Y + B) to eliminate the denominator.
- This gives us Y + A = 2(1.5Y + B).
- Simplifying, we get Y + A = 3Y + 2B.
- Rearranging the equation, we have A - 2B = 2Y.

Step 5: Calculate the investment ratio after 18 months
- Divide the profit share of P by the profit share of Q to get the investment ratio.
- (Y + A) / (1.5Y + B) = 17220 / 11070.
- Substitute the value of A - 2B from Step 4 into this equation.
- This gives us 2Y / (1.5Y + B) = 17220 / 11070.

Step 6: Calculate the value of B
- Cross multiply and solve the equation to get B.
- 2Y * 11070 = 17220 * (1.5Y + B).
- Simplifying, we get 22140Y = 17220 * 1.5Y + 17220B.
- 22140Y - 25830Y = 17220B.
- -3680Y = 17220B.
- B = -3680Y / 17220.

Step 7: Calculate the percentage increase in Q's investment
- To find the percentage increase, we need to compare the additional investment by Q with his initial investment.
- Percentage Increase = (B / 1.5Y) * 100.
- Substitute the value of B from Step 6 into this equation.
- Percentage Increase = (-3680Y / 17220) / (1

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