P,Q and R enter into a partnership with capitals in the ratio 3:2:1. After 4 months, P leaves the business and after 4 more months Q also leaves the business and R continues till the end of the year. If R takes 10% of the profit for managing the business, then what part of the profit does R get?
Answer: A Let Rs 100 be the profit. Rs 90 is to be divided in the ratio 12:16:12. i.e 3:4:3 R gets 3/10 * 90 = 27 and 10 for managing. => Thus, 27+10 = 37%.
Q. No. 2:
Rs 4830 is divided among Abhishek, Dishant and Prashant such that if Abhishek's share diminishes by Rs 5, Dishant's ahre diminishes by Rs 10 and Prashant's share diminishes by Rs 15, their shares will be in the ratio 5:4:3. Find the Dishant's original share?
Answer: A Let actual share of Abhishek, Dishant and Prashant be A, D , P respectively. A+D+P = 4830. Hence, A's, D's and P's share are diminished by Rs 5, Rs 10 and Rs 15, their nes share will be rs 4800. Dishant's diminished share = 4/12 * (4800) = Rs 1600. Hence, Dishant actual share = Rs 1600+ Rs 10 = Rs 1610.
Q. No. 3:
On a certain day, the ratio of the passenger in the 1st class and the second class travelling by train is 1:3. the ratio of the fares collected from each first class and second class passengers is 30:1. If the total amount collected from all the passengers is Rs 1,320. Find the amount in Rs, collected from the second class passengers.
Answer: D Let the number of passengers travelling by first class and second class be x and 3x respectively. Lets the fares collected from each of the first class and second class passengers be 30y and y respectively. Hence x(30y) +3x(y) = 30xy +3xy = 33xy = 1320 xy = 40. total amount collected from the second class = 3xy = 3*40 = Rs 120.
Q. No. 4:
20% of the students in a class failed in an examination. Out of the students who failed, 75% were males. Male students who failed constitute 90% of the economically poor students in the class. What is the ratio of the number of economically poor students to the number of students in the class?
Answer: A Let the total number of students in the class be 't' Let total number of students in the class who are economically poor be 'p' Total number of students who failed = t/5 Total number of male students who failed = 3/4 * t/5 = 9p/10 => p/t = 1/6. => Number of economically poor students/ Number of Students = 1/6.
Q. No. 5:
An outgoing batch of students want to gift a PA system worth Rs 4,200 to their school. If the teachers, offer to pay 50% more than the students, and an external benefactor gives three times the teacher's contribution, then how much should the teachers donate?
Answer: C The ratio of the share students : teacher: benefactor = 1: 1.5 : 4.5. So the proportion to teacher's share = 1.5/7 Hence, the teachers would donate = 1.5/7 * 4200 = Rs 900.
Q. No. 6:
Points A and B are both in the line segment PQ and on the same side of its midpoint. A divides PQ in the ratio 2:3, and B divides PQ in the artio 3:4. If AB =2, then the length of PQ is
Answer: A Let PA =2x and AB = 3x and PB = 3y and BQ = 4y PB:BQ = 3:4 PA: QA = 2:3 PQ = 5x =7y x= 7/5 y..........(i) Now, AB = PQ - PA - BQ = 7y-4y-2x => 3y-2x =2............(ii) From equation i and ii, y= 10 and Hence, PQ = 70.