Quantity -I: P and Q started a business together with an initial investment of Rs. 4000 and Rs. 3200, respectively. After 4 months, R joined with an investment 25% more than Q. After 4 more months, P and Q infused additional amount of Rs. 500 and Rs. 800, respectively. Find the profit share of B if the total profit is Rs. 13860 after a year.

Quantity -II: Suresh, Anil and Vishal can complete a task in 8 days while working together. Anil alone can complete the work in 24 days, and ratio of efficiency of Suresh and Vishal is 1: 3. If they are entitled to receive a total of Rs. 10800, find the share of Anil.

Quantity -III: Aditi bought an article and sold it for Rs. 4000 at a profit of 25%. At what price it should be sold to earn a profit of 30%?

Solution

Quantity -I: Initial Investment of P = Rs. 5000 Initial Investment of Q = Rs. 4000 Initial Investment of R = 4000 × 1.25 = Rs 5000 After 8 months, Total investment of P = 5000 + 500 = Rs. 5500 Total investment of Q = 4000 + 800 = Rs. 4800 Ratio of share of profit of P: Q: R = (5000 × 8 + 5500 × 4): (4000 × 8 + 5000 × 4): (5000 × 8) = 31: 26: 20 Therefore, profit share of Q = [26/ (31 + 26 + 20)] × 13860 = Rs. 4680 Quantity -II: Let, time taken by Suresh and Vishal working together be x days. According to question, 1/x + 1/24 = 1/8 1/x = 1/8 – 1/24 1/x = (3 – 1)/24 1/x = 2/24 x = 24/2 = 12 days So, time taken by Suresh to complete the work = 12 × (1 + 3)/1 = 48 days So, time taken by Vishal to complete the work = 12 × (1 + 3)/3 = 16 days Therefore, ratio of efficiency of Anil, Suresh and Vishal = (1/24): (1/48): (1/16) = 2: 1: 3 Therefore, share of Anil = [2/(2 + 1 + 3)] × 10800 = Rs. 3600 Quantity -III: Cost price of article = 4000/1.25 = Rs. 3200 So, selling price of article = 4000 × 1.30 = Rs. 5200 Therefore, Quantity I > Quantity II < Quantity III