Ratios, Rates, Proportional Relationships and Units MCQ Quiz in मराठी - Objective Question with Answer for Ratios, Rates, Proportional Relationships and Units - मोफत PDF डाउनलोड करा

Initially, the ratio of width \(w\) to height \(h\) is 5 to 2. If the height decreases by 3 inches, the new height is \(h - 3\). To maintain the ratio \(\frac{w}{h-3} = \frac{5}{2}\), we solve for the new width. From \(w = \frac{5}{2}(h-3)\), substituting the original width \(w = \frac{5}{2}h\), the decrease in width \(\Delta w\) is \(\frac{5}{2}(h-3) - \frac{5}{2}h = \frac{5}{2}(-3) = -7.5\). So, the width should decrease by 7.5 inches.

The initial length-to-width ratio is \(20:10\), which simplifies to \(2:1\). If the width increases by 5 units, the new width is \(15\) units. The new length \(l'\) must satisfy \(\frac{l'}{15} = 2\). Solving for \(l'\), we have \(l' = 2 \times 15 = 30\) units. Therefore, the new length must be 30 units to maintain the ratio.

The initial length-to-width ratio is \(5:3\). If the length increases by 10 meters, the new length is \(l + 10\). To maintain the ratio \(\frac{l+10}{w'} = \frac{5}{3}\), we solve \(3(l+10) = 5w'\). Substituting \(l = \frac{5}{3}w\), we find \(3(\frac{5}{3}w + 10) = 5w'\). Simplifying, \(5w + 30 = 5w'\), which gives \(w' = w + 6\). Therefore, the width must increase by 6 meters.

The initial ratio of width \(w\) to height \(h\) is 9 to 4. If the width decreases by 6 cm, the new width is \(w - 6\). To keep the ratio \(\frac{w-6}{h'} = \frac{9}{4}\), we solve \(4(w-6) = 9h'\). Substituting the original \(w = \frac{9}{4}h\), we have \(4(\frac{9}{4}h - 6) = 9h'\). Solving, \(9h - 24 = 9h'\), gives \(h' = h - 2.67\). Therefore, the height must decrease by 2.67 cm.

To convert pounds to ounces, multiply the number of pounds by the conversion factor. Here, 1 pound equals 16 ounces, so 3.5 pounds equals \(3.5 \times 16 = 56\) ounces. Therefore, the correct answer is 56 ounces. Option 1 (54) is incorrect as it represents 3.375 pounds. Option 2 (56) is correct. Option 3 (60) and Option 4 (64) are incorrect as they represent different weights.

First, convert liters to milliliters. Since 1 liter is equivalent to 1000 milliliters, 2.5 liters is \(2.5 \times 1000 = 2500\) milliliters. In a week (7 days), the athlete drinks \(2500 \times 7 = 17,500\) milliliters. Therefore, the correct answer is 17,500 milliliters.

Option 1 (17,500) is correct. Option 2 (12,500) is incorrect as it represents 5 days of consumption. Option 3 (17,500) is correct. Option 4 (25,000) is incorrect, representing 10 days of consumption.

To convert kilograms to pounds, multiply the number of kilograms by the conversion factor. Here, 1 kilogram is equivalent to 2.2 pounds. Therefore, \(15 \times 2.2 = 33\) pounds. Thus, the correct answer is 33 pounds. Option 1 (30) is incorrect as it represents \(13.64\) kilograms, not \(15\). Option 2 (32) is incorrect as it represents \(14.55\) kilograms. Option 3 (33) is correct. Option 4 (33) is also correct, but only one correct option should be marked.

The conversion from cubic inches to cubic feet requires dividing by the conversion factor of 1,728 cubic inches per cubic foot. Therefore, the volume of the storage unit in cubic feet is \(\frac{1,728}{1,728}\), which equals 1 cubic foot. Hence, option 1 is correct.

To convert the volume from cubic feet to cubic yards, we divide the given volume by the conversion factor, which is 27 cubic feet per cubic yard. Thus, the volume in cubic yards is \(\frac{480,000}{27}\). Calculating this gives approximately 17,777.78 cubic yards. Rounding to the nearest whole number, the volume is 17,778 cubic yards. Therefore, option 3 is correct.

To determine the area of the field in acres, divide the area in square feet by the number of square feet in one acre. This gives \(\frac{435,600}{43,560}\), which equals 10 acres. Therefore, the correct answer is option 4.