A sum was put at simple interest at a certain rate for 2 years. Had it been put at 3% higher rate, it would have fetched Rs 300 more. The sum is
None of these
Answer: Option C. Increase of 3% fetched Rs.300 more. It is for 2 years. For 1 year Increase of 3% will fetch Rs.150. So 1 % will fetch Rs.50 100% = 5000.
A sum of Rs 1,550 was lent partly at 5% and partly at 8% per annum simple interest. The total interest received after 3 years was Rs 300. The ratio of money lent at 5% to that lent at 8% is
Answer: Option D. Partly division of 1550 is x and x - 1550 5 % of x + 8 % of (1550 – x) = 0.05x + 0.08(1550 – x) For 3 years, the total interest is 300. 3[0.05x + 0.08(1550 – x)] = 300 x = 800 and 1550 – x = 750 The ratio of money = 16:15.
The difference between the simple interest received from two different sources on Rs 3 lakhs for 2 years is rs 1,500. The difference between their rates of interest is
Answer: Option C. Let x and y be the interest rates. x% of 3 lakhs – y% of 3 lakhs = 1500 (x– y) % of 3 lakhs = 1500 300000(x – y)/100 = 1500 (x – y) = 0.5% for 2 years For 1 year = 0.25%
A square tin sheet of side 12 cm is converted into a box with open top in the following steps: The sheet is placed horizontally. Then, equal-sized squares, each of side x cm, are cut from the four corners of the sheet. Finally, the four resulting sides are bent vertically upwards in the shape of a box. If x is an integer, then what value of x maximizes the volume of the box?
Answer: Option D.
Volume of the box = l × b × h = (12 – 2x) (12 – 2x) (x) Putting x = 1, 2, 3, 4, we get the maximum value of the above equation at x = 2. So maximum v = 128. i.e. 4th option
A spherical ball of lead, 3 cm in diameter is melted and recast into three spherical balls. The diameter of two of these is 1.5 cm and 2 cm respectively. The diameter of the third ball is
Answer: Option C. The sum of the volumes of the new balls will equal the volume of the original ball. So, 1.53 = 0.753 + 13 + r3. Solving this equation gives r = 1.25 So, d = 2.5 cm.
A cylinder is filled to 4/5th of its volume. It is then tilted so that the level of water coincides with one edge of its bottom and top edge of the opposite side. In the process, 30 cc of the water is spilled. What is the volume of the cylinder?
Answer: Option B. When tilted, the water level will form the diagonal of the tank and the volume of the water will he half that of the cylinder. Suppose the volume of the cylinder is V. Since 30 ml = 30 cc has spilled out, 4V/5 = 1/2 V + 30. Solving this equation gives V = 100 cc.
A and B invest Rs 3 lakhs and Rs 4 lakhs in a business. A receives Rs 1,000 per month out of the profit as a remuneration for running the business and the rest of profit is divided in proportion to the investments. If in a year 'A' totally receives X 39,000, what does B receive?
Answer: Option C. A and B invest in the ratio 3 : 4. A receives 1000 per month so he will get 12000 for a year. If A receives 39000 in total then 39000 – 12000 = 27000 will be his share. If 3x = 27000, then 4x = 36000.
In a partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time and C, the rest of the capital for whole time. Find A's share of the total profit of Rs 2,300.
Answer: Option C Let the total capital is 6 and time is also 6 years. A invests 1 for 1 year. B invests 2 for 2 years Then, C invests 6 – (1 + 2) = 3 for 6 years. The ratio of investment is A : B : C = 1 : 4 : 18 If total profit is Rs 2300 then A's share = 1/23 x 2300 = Rs 100
A, B and C enter into a partnership by investing in the ratio of 3 : 2 : 4. After one year, B invests another Rs 2,70,000 and C, at the end of 2 years invests Rs 2,70,000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find the initial investment of A, B and C.
Rs 2,70,000; Rs 80,000 and Rs 3,60,000
Rs 1,70,000; Rs 1,80,000 and Rs 3,60,000
Rs 2,70,000; Rs 1,80,000 and Rs 3,60,000
Rs 2,70,000; Rs 1,80,000 and Rs 3,00,000
Answer: Option C. 1st year, A = 3x, B = 2x and C = 4x 2nd year, A = 3x, B = 2x + 270000 and C = 4x 3rd year, A = 3x, B = 2x + 270000 and C = 4x + 270000 Total investment by A, B and C is A = 3x + 3x + 3x = 9x B = 2x + 2x + 2x + 270000 + 270000 = 6x + 540000 C = 4x + 4x + 4x + 270000 = 12x + 270000 After three years the ratio is 3 : 4 : 5 x = 90000. Thus initial investment = (3 * 90000): (2 * 90000): (4 * 90000) ` 270000, ` 180000, ` 360000
Two vessels contain mixtures of milk and water in the ratio of 8 : 1 and 1 : 5 respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture must be drawn from the second vessel to fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?
Answer: Option C. The ratio of milk to total volume of the mixture in the 3 vessels is 8/9, 1/6 and 1/2 respectively. We can consider these values as 16/18, 3/18 and 9/18 respectively. By alligation, we get the ratio in which the two mixtures are mixed as 6:7 respectively. Since the total quantity is 26, the quantity from the 2nd vessel is (7/13) * 26 = 14 gallons.