1. Sea water contains 5% salt by weight. How many kg of fresh water must be added to 40 kg of sea water for the salt content of the solution to be 2%?
Ans:1 There is 5% of salt in 40 kg of sea water So, amount of salt in 40 kg of sea water is = 5/100 * 100 = 2 kg Let the amount of fresh water need to be added be x kg 2kg/(40+x)kg = 2% = 2/100 100 = 40 + x X = 60kg
2. The breadth of a rectangle is three-fourth of its length. The area of rectangle is 1728m2. Find the perimeter of the rectangle?
Ans:5 Let length = ‘L’ Breath = ‘B’ = 3L/4 Area = L*B = L*3L/4 = 3L2/4 = 1728 L2 = 2304 L = 48 and B = 36 Perimeter = 2(L+B) = 168m
3. Present ages of SRK and Akshay are in the ratio of 6:5. After 4 years, the ratio of their ages become 10:9 respectively. Calculate the present age of SRK?
Ans:1 Let SRKs age be 6x and Akshays age be 5x, (6x+4)/(5x+4) = 10/9 54x + 36 = 50x + 40 => x = 1 => SRK’s age = 6*1= 6 years.
4. Pawan and Arun started a business with an initial investment of Rs.5000 and Rs.4500 respectively. Pawan adds Rs.250 after 6 months while Arun adds Rs.500 after every 4 months. They used their amount of profit received from the first business at the end of 1 year to start another business. If the ratio of profit from the second business is 41 : 36, then find the ratio of time for which they invested their capital in second business?
Ans:2 Ratio of profit from the first business = (5000 * 6 + 5250 * 6) : (4500 * 4 + 5000 * 4 + 5500 * 4) => 61500 : 60000 = 41 : 40 In second business: Let the amount invested by Pawan be 41x for a time period of T1 Let the amount invested by Arun be 40x for a time period of T2 Ratio of profit from second business = (41x * T1): (40x * T2) = 41: 36 (41x * T1)/ (40x * T2) = 41/ 36 T1/T2 = 10/9 Required ratio = T1: T2 = 10 : 9
5. In a competitive exam, the minimum passing percentages for XL and Unreserved are 25% and 45% respectively. An Unreserved candidate scored 83 marks and failed by 25 marks. What is the minimum passing marks for XL?
Ans:3 Passing marks for the Unreserved category = 83 + 25 = 108 ∴ 45% of the total marks = 108 => Total marks = 108/0.45 = 240 ∴ Passing marks for XL category = 0.25 * 240 = 60
6. A book was sold for Rs. 276 with a profit of 15 %. If it were sold for Rs. 255, then what would have been the percentage profit or loss?
7. Calculate the percentage decrease in consumption of an article if the price is increased by 20% and expenditure is kept same.
Ans:1 Let price = 100 Consumption = 100 New price = 120 New Consumption = x 100*100 = 120*x x = 100*100/120 250/3 Percentage decrease = (100-250/3)/100 * 100 = 50/300 * 100 = 50/3% SHORTCUT Percentage decrease in consumption = (a/(100+a))*100 a = 20% Percentage decrease in consumption = 20/120 * 100 = 50/3%
8. Total interest received from a sum of Rs.12250 at the end of 4 years at certain rate of simple interest is Rs.840 more than the interest received from another sum of Rs.21000 at the end of 2 years at the same rate of simple interest. Find the rate of interest.
Ans:1 Let the interest = R% Interest received from first sum = (12250 * R * 4)/100 = 490R Interest received from second sum = (21000 * R * 2)/100 = 420R According to question- => 490R – 420R = 840 => 70R = 840 => R = 12%
9. A boat takes 12 minutes to row a distance of 10km upstream and it takes 6 minutes to row the same distance downstream. Calculate the speed of boat in still water.
Ans:2 Speed of boat upstream in km/h = 10/12 * 60 = 50 km/h Speed of boat downstream in km/h = 10/6 * 60 = 100 km/h Speed of boat in still water = (50 + 100) /2 = 75 Km/h
10. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. How many days B alone will take to finish the work?
Ans:1 Let’s suppose A takes 6n days to finish the work hence B will take 3n days and C will take 2n days to finish the work. Let’s suppose total work = 1 unit Hence; 1/6n+1/2n+1/3n=1/2 => 1/n=1/2 => n = 2 Hence time taken by B = 3n days = 6 days
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