Instructions: DO NOT USE CALCULATOR. Figures are not drawn to scale. Arif has x marbles of which 20% are black and 80% are red. Babu has y marbles of which 40% are black and 60% are green. Dipu has z marbles of which 50% are black and 50% are blue. If 25% of the total marbles they have are black, what is x?
A. \(y + 3z\)
B. \(3y + 5z\)
C. \(4y + 5z\)
D. \((y+5z)/2\)
E. none of these
Explanation: (E) Total black marbles = \(0.20x + 0.40y + 0.50z\). Total marbles = \(x + y + z\). Given: Total black marbles are 25% of the total marbles: \(0.20x + 0.40y + 0.50z = 0.25(x + y + z)\). Multiply by 100 to clear decimals: \(20x + 40y + 50z = 25x + 25y + 25z\). \(40y - 25y + 50z - 25z = 25x - 20x\). \(15y + 25z = 5x\). Divide by 5: \(3y + 5z = x\). So, \(x = 3y + 5z\). Since \(3y + 5z\) is not an option, the answer is E.
Related Questions (Any University/Year)
- The members of an association decided to contribute equally to create a fund of Tk. 45,000. Five members refused to contribute, so each of the other members had to contribute additional tk. 15 for that fund. How many members were there in the association?
- 3x+y=18, and x+3y=1.Find the value of 2x+2y
- How many flowers are there if all of them are roses except two, all of them are tulips except two and all of them are daisies except two?
- The cost price of a table and a chair together is TK. 690. If the table costs 30% more than the chair, then find the cost price of the table and the chair respectively.
- Working independently, Sourodip can perform a certain task in 6 hours and Eshanee can perform it in 7 hours. If Sourodip and Eshanee work together for 3 hours, and then Sourodip leaves, how many hours will it take Eshanee to complete the task alone?
- ডাক্তার রোগীকে প্রতি ২ ঘন্টা পর পর খাওয়ার জন্য ৬টি বড়ি দিলেন। শেষ বড়িটি রোগী কত ঘণ্টা পরে খাবেন?
- In a sports club with 30 members, 17 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis?
- A room at Zaber Hotel International can accommodate 4 people. The rate is 3900 one person and Tk. X for each additional people. If 3 people take the room for one night and pays Tk. 2100 per person, what is the value of X?
- The average age of a man and his son is 20. After 10 years, their age will be in the ratio 2:1. What was the age of the man and his son 5 years ago respectively?
- The ratio between sumit's and Prakash's age at present is 2:3. Sumit is 6 years younger than Prakash. The ratio of Sumit's age to Prakash's age after 6 years will be.
- If y% of x is 29. Then x =?
- 40% of students in a class are smart. The rest are stupid. Half the students play sports and half don't. If 20% of the students are smart and play sports, what percent of the students are stupid and don't play sports?
- Rashid deposits Tk. 1200 from his salary in the first month. In every subsequent month, he deposit Tk. 100 more than the amount deposit in the previous month. What will be the total amount of his deposit in 18 months?
- In a party of 77 people, there are twice as many women as children and twice as many children as men. How many children were present?
- B and C are points on a straight line AD where AB=BC=CD. What percent of AC is AD?
- The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 9 consecutive integers that start with n (in terms of m)?
- আয়তক্ষেত্রের বাহুগুলােকে 20% বর্ধিত করলে এর ক্ষেত্রফল কত শতাংশ বৃদ্ধি পাবে?
- The product of two numbers is 72. If 24 is their LCM what is their HCF?
- A certain machine fills a bag with 7 ounces of potato chips in 3.5 seconds. At this rate how many seconds will it take the machine to fill a bag with 15 ounces of potato chips?
- খুলনা বিশ্ববিদ্যালয় হতে রূপসা ব্রীজ পর্যন্ত সরল পথে ৪০ মিটার ব্যবধানে লাইট পোষ্ট স্থাপন করা আছে। প্রথম থেকে নবম পোষ্ট পর্যন্ত প্রতি মিটার ৩০০০ টাকা ব্যয়ে ড্রেন নির্মাণ করতে গেলে কত টাকা লাগবে?