Direct proportion means two quantities increase or decrease together at the same rate, while indirect proportion means one increases as the other decreases. These relationships help us solve problems involving speed, work, cost, and many real-life situations. Understanding proportion is useful in cooking, construction, and comparing quantities in everyday tasks. This Direct and Indirect Proportion Quiz for Grade 8 provides practice with identifying and solving proportion problems. By attempting these 10 MCQs, students can check how well they understand and can apply direct and indirect proportion.
A machine that can perform a task in 15 hours operates at a speed directly proportional to the square of its efficiency. If the efficiency of the machine is increased by 20%, how much time will it now take to complete the task?
Answer: (d) 10.42 hours
How many men are required to finish a task that is three times larger than the original, if the new task must be completed in 24 days with each man working 8 hours daily? The original task was completed by 16 men in 8 days working 12 hours a day.
Answer: (a) 24
A contractor estimates that 4 workers could paint a building in 14 days. If he decides to use 7 workers instead of 4, how long should they take to complete the job?
Answer: (c) 8 days
A cyclist covers a certain distance at a certain speed. If she increases her speed by 20%, then she takes 10 minutes less to cover the same distance. Find the time taken by her initially to cover the distance traveling at the original speed.
Answer: (b) 1 hour
A camp has enough provisions for 1000 soldiers for 40 days, with each soldier consuming 4 kg of provisions per day. After 10 days, 200 more soldiers join the camp, and the daily consumption per soldier increases by 25%. If the remaining provisions are to be shared equally among the new total number of soldiers with the increased consumption rate, how many days will the provisions last after the 10th day?
Answer: (c) 20 days
A company produces gadgets using two different machines, X and Y. Machine X can produce 81 gadgets in 3 hours, while Machine Y can produce 121 gadgets in 11 hours. If Machine X's production is inversely proportional to the square root of the number of gadgets it produces, and Machine Y's production is directly proportional to the square root of the number of gadgets it produces, how long will it take Machine X to produce the same number of gadgets as Machine Y if both machines operate for the same amount of time?
Answer: (b) 15 hours
When a person walks, the pressure P on each boot sole varies inversely with the area A of the sole. Denise is walking through deep snow, wearing boots that have a sole area of 29 m2 each. The boot-sole pressure is 4 pa/m2 when she stands on one foot. The constant of variation is Denise's weight in pascal. What is the snowshoe pressure when she stands on one foot, If Denise wears snowshoes, each with an area 3.5 times that of her boot soles?
Answer: (d) 1.14 pa/m2
The extension in an elastic spring varies directly with the weight hung on it. If a weight of 120 grams produces an extension of 3.6 cm and a weight of 200 grams produces an extension of 6 cm, proportionality constant remains the same. What weight will produce an extension of 18 cm?
Answer: (c) 600 g
Read the following passage and answer the following question: In academic settings, students often notice that their performance on exams is related to the amount of time they spend studying. Generally, there is a direct relationship between study time and exam performance. On the other hand, there is an inverse relationship between the number of distractions and exam performance. As distractions increase, the ability to concentrate decreases, leading to poorer results. Moreover, the effectiveness of studying is also inversely proportional to fatigue levels. The more tired a student becomes, the less effective their study sessions are. If the student studies for 7 hours, has 5 distractions and a fatigue level of 6, find the required increase in study time that would double the student’s performance.
Answer: (a) 7 hours
Read the following passage and answer the following questions: A person embarks on a journey from London to Manchester, a city located 360 km away. He departs from London at 7:00 a.m. and arrives in Manchester at 1:00 p.m. After resting for half an hour, he starts his return journey to London at 1:30 p.m. The person finally reaches London at 9:00 p.m. If the person maintained a uniform speed during both parts of the journey, there is a noticeable decrease in his speed while traveling back to London. The task is to calculate the difference in his speed during the return trip compared to the journey to Manchester. If the person increased his speed by 20% during the return journey compared to his speed while going to Manchester, how much time would he take for the return trip, and at what time would he reach London?
Answer: (a) 6:30 p.m.
