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4067+ MCQ Questions in english हिन्दी
A shopkeeper mixes two varieties of pulses worth Rs. 50/kg and Rs. 75/kg to get a mixture worth Rs. 65/kg. In what ratio should they be mixed?
Using the alligation rule: $ (75 - 65) : (65 - 50) = 10 : 15 = 2 : 3 $. Thus, the ratio of cheaper (50/kg) to dearer (75/kg) is 3:2, or dearer to cheaper is 2:1
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If the cost of apples increases by 20% and then decreases by 20%, what is the net percentage change?
Let the original price be 100. After a 20% increase, price = $ 100 \times 1.2 = 120 $. After a 20% decrease, price = $ 120 \times 0.8 = 96 $. Net change = $ \frac{96 - 100}{100} \times 100 = -4\% $.
A car travels 275 km at 50 km/h and 315 km at 70 km/h. What is the average speed for the entire journey
Total distance = 275 + 315 = 590 km. Time for the first part = $ \frac{275}{50} = 5.5 $ hours; second part = $ \frac{315}{70} \approx 4.5 $ hours. Total time = $ 5.5 + 4.5 = 10 $ hours. Average speed = $ \frac{590}{10} = 59 $ km/h (approximately 58.33 km/h for precision).
A sum of Rs. 25,000 amounts to Rs. 31,000 in 4 years at simple interest. What is the rate of interest?
Simple Interest (SI) = Amount - Principal = 31,000 - 25,000 = 6,000. Using the formula $ SI = \frac{P \times R \times T}{100} $, we get $ 6,000 = \frac{25,000 \times R \times 4}{100} $. Solving, $ R = 6\% $.
The sum of two numbers is 90, and one of them exceeds the other by 16. What is the smaller number?
Let the smaller number be $ x $. Then the larger number is $ x + 16 $. Given $ x + (x + 16) = 90 $, we solve: $ 2x + 16 = 90 $, so $ 2x = 74 $, and $ x = 37 $. Thus, the smaller number is 37.
If 2x + 3y = 12 and 3x - 2y = 5, what is the value of x + y?
Add the equations: (2x + 3y) + (3x - 2y) = 12 + 5. This gives 5x + y = 17. Subtract: (2x + 3y) - (3x - 2y) = 12 - 5, giving -x + 5y = 7. Solve the system: x = 3, y = 1. Thus, x + y = 4. **What is the value of x if 2x + 3 = 7ostrar
The difference between two numbers is 30, and the smaller number is 13 more than half of the greater number. What is the greater number?
Let the greater number be x, smaller number be y. Given x - y = 30 and y = (x/2) + 13. Substitute y in the first equation: x - (x/2 + 13) = 30. Solving, x/2 = 43, so x = 86.
If x + y + z = 0, then what is the value of (x²/yz) + (y²/xz) + (z²/xy)?
Since x + y + z = 0, we can use algebraic manipulation. The expression simplifies to (x³ + y³ + z³)/(xyz). Since x + y + z = 0, x³ + y³ + z³ = 3xyz. Thus, the value is 3xyz/xyz = 3. However, rechecking the options and problem context, the correct simplification yields 0 in some cases due to cancellation (common UPSC trick).
A shopkeeper mixes two varieties of pulses worth Rs. 50/kg and Rs. 75/kg to get a mixture worth Rs. 65/kg. In what ratio should they be mixed?
Using the rule of alligation: (75 - 65) : (65 - 50) = 10 : 15 = 2 : 3. The ratio of cheaper to dearer is 3:2, so the answer is 2:1 for dearer to cheaper.
If the cost of apples increases by 20% and then decreases by 20%, what is the net percentage change?
Let original price = 100. After 20% increase, price = 120. After 20% decrease, price = 120 × 0.8 = 96. Net change = (96 - 100)/100 × 100 = -4%.
A car travels 275 km at 50 km/h and 315 km at 70 km/h. What is the average speed for the entire journey?
Total distance = 275 + 315 = 590 km. Time for first part = 275/50 = 5.5 hours; second part = 315/70 = 4.5 hours. Total time = 5.5 + 4.5 = 10 hours. Average speed = 590/10 = 59 km/h (approx. 58.33 km/h).
Simple Interest (SI) = Amount - Principal = 31,000 - 25,000 = 6,000. SI = PRT/100, so 6,000 = (25,000 × R × 4)/100. Solving, R = 6%.
Simple Interest (SI) = Amount - Principal = 31,000 - 25,000 = 6,000. SI = PRT/100, so 6,000 = (25,000 × R × 4)/100. Solving, R = 6%.
A sum of Rs. 25,000 amounts to Rs. 31,000 in 4 years at simple interest. What is the rate of interest?
Simple Interest (SI) = Amount - Principal = 31,000 - 25,000 = 6,000. SI = PRT/100, so 6,000 = (25,000 × R × 4)/100. Solving, R = 6%.
The sum of two numbers is 90, and one of them exceeds the other by 16. What is the smaller number?
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