Question
In the question, four Quantity I, Quantity II, Quantity
III, and Quantity IV are given. You have to solve all the four Quantities and establish the correct relation between these quantities and choose the correct option. Quantity I : An article is sold at a profit of 28%. If its selling price is Rs. 5760, determine the cost price. Quantity II: Two people, K and M, start a business. K invests Rs. (c – 400) and M invests Rs. c. After 5 months, K adds Rs. 400 more, while M withdraws Rs. 1000. At the end of the year, K’s share of the profit is Rs. 4140 out of the total Rs. 7830. Find the initial investment of M. Quantity III: A man X spends 10% of his income on food, 20% on clothes, (n – 2)% on luxury, and 12% on rent. From what remains, he donates 40% and saves Rs. 1440. If the amount spent on luxury is Rs. 1080, calculate 2n% of X’s total income. Quantity IV: The simple interest for 3 years at 12% per annum and the compound interest for 2 years at 12% per annum differ by Rs. 528. If the same principal is invested in both cases, find the principal amount.Solution
ATQ, Quantity I: Required cost price of the item = (5760/1.28) = Rs. 4500 So, Quantity I = Rs. 4500 Quantity II: Profit share ratio of K and M: = {(c - 400) X 5 + c X 7}:{c X 5 + (c - 1000) X 7} = (12c - 2000) :(12c - 7000) = (6c - 1000) :(6c - 3500) ‘M’ profit share = 7830 - 4140 = Rs. 3690 ATQ; (6c - 1000/(6c - 3500) = (4140/3690) (6c - 1000) /(6c - 3500) = (46/41) 246c - 41000 = 276c - 161000 30c = 120000 'c' = 4000 Initial investment of ‘M’ = Rs. 4000 So, Quantity II = Rs. 4000 Quantity III: Let the total income of ‘X’ be Rs. 100t So, 100t X {(n - 2) /100} = 1080 Or, t(n - 2) = 1080 ------------- (I) Total amount spent by ‘X’ = 10t + 20t + 1080 + 12t = 42t + 1080 Remaining amount with ‘X’ = 100t - 42t - 1080 = 58t - 1080 Now, (58t - 1080) X 0.6 = 1440 34.8t - 648 = 1440 34.8t = 1440+ 648 34.8t = 2088 't' = 60 Income of ‘X’ = 100 X 60 = Rs. 6000 Now,  t(n - 2) = 1080 n - 2 = (1080/60) n = 18 + 2 'n' = 20 So, required amount = 40% of 6000 = 0.4 X 6000 = Rs. 2400 So, Quantity III = Rs. 2400 Quantity IV: Let the invested principle be Rs. 'P' Simple Interest for 3 years = P X 12 X 3 / 100 = 0.36P Compound Interest for 2 years = P X [(1.12)² - 1] = P X 0.2544 ATQ; 0.36P - 0.2544P = 528 0.1056P = 528 'P' = (528/0.1056) = Rs. 5000 So, Quantity IV = Rs. 5000 So, Quantity-I > Quantity-II > Quantity III < Quantity IV
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