Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
111
A garrison has provisions for X men for 50 days. After 15 days, 100 men join, and the food then lasts for 25 days. Find X.
Answer:
250
Remaining food after 15 days is for X men for 35 days (X × 35). It lasts (X + 100) men for 25 days. Equation: 35X = 25(X + 100) => 35X = 25X + 2500 => 10X = 2500 => X = 250.
112
A garrison has provisions for X men for 40 days. After 10 days, 50 men leave, and the remaining food lasts for 36 days. Find X.
Answer:
300
Remaining food after 10 days is meant for X men for 30 days (X × 30). It actually lasts (X - 50) men for 36 days. Equation: 30X = 36(X - 50) => 30X = 36X - 1800 => 6X = 1800 => X = 300.
113
120 men have provisions for 30 days consuming 900g a day. For how many days will the same provisions last for 150 men consuming 600g a day?
Answer:
36 days
Total provisions = 120 × 30 × 900 = 3,240,000 grams. D2 = 3,240,000 / (150 × 600) = 3,240,000 / 90,000 = 36 days.
114
A fort has food for 400 men. After 20 days, 100 men join, and the food then lasts for 24 days. How many days was the food initially meant to last?
Answer:
50 days
After 20 days, food left lasts 500 men for 24 days. Remaining food = 500 × 24 = 12000 man-days. For 400 men, it would last 12000 / 400 = 30 days. Initial days = 20 + 30 = 50 days.
115
A garrison has food for 300 men for a certain number of days. After 15 days, 100 men leave, and the food then lasts for 30 days. Find the initial number of days.
Answer:
35 days
After 15 days, food left lasts 200 men for 30 days. Remaining food = 200 × 30 = 6000 man-days. For 300 men, this would have lasted 6000 / 300 = 20 days. Initial total days = 15 + 20 = 35 days.
116
A garrison has provisions for a certain number of days for 200 men. After 10 days, 50 men join the garrison, and the food then lasts for 20 days. Find the initial number of days the food was meant to last.
Answer:
35 days
After 10 days, remaining food lasts 250 men for 20 days. Remaining food = 250 × 20 = 5000 man-days. For 200 men, 5000 man-days would last 5000 / 200 = 25 days. Total initial days = 10 (passed) + 25 (remaining) = 35 days.
117
500 men have provisions for 28 days at 600g per day. How many men can be fed for 35 days at 400g per day from the same provisions?
Answer:
600
Total provisions = 500 × 28 × 600 = 8,400,000 grams. Required men = 8,400,000 / (35 × 400) = 8,400,000 / 14,000 = 600 men.
118
A stock of food is enough for 300 men for 40 days at 750g per day. If there are 400 men and the daily ration is reduced to 500g, how many days will the food last?
Answer:
45 days
Total food = 300 × 40 × 750 = 9,000,000 grams. D2 = 9,000,000 / (400 × 500) = 9,000,000 / 200,000 = 45 days.
119
150 men have food for 45 days at 600g per head per day. How many days will the food last for 250 men at 540g per head per day?
Answer:
30 days
Total food = 150 × 45 × 600 = 4,050,000 grams. For 250 men at 540g, D2 = 4,050,000 / (250 × 540) = 4,050,000 / 135,000 = 30 days.
120
A garrison of 200 men has provisions for 36 days at the rate of 500g per day per man. For how many days will the provisions last for 300 men at the rate of 400g per day per man?
Answer:
30 days
Total provisions = M1 × D1 × R1 = 200 × 36 × 500 = 3,600,000 grams. If 300 men consume 400g daily, D2 = 3,600,000 / (300 × 400) = 3,600,000 / 120,000 = 30 days.