56.

How many days will it take for A alone to complete the job?

 A. 8 B. 6 C. 10 D. 20
Answer:--Select--
Explanation: Now if we try to eliminate choices in this question, we know that A and B together take 6 days to complete the job. Therefore, A alone will take more than 6 days to complete the job. Therefore, we can eliminate answer choice (2). In any question, as a rule spend about 5 seconds to see if the answer choices provide any clue to solve the question or help in eliminating one or more obviously absurd choices. This will help you (1) in reducing the time it will take to do the problem and (2) in increasing your probability of success should you choose to take a guess without actually solving the problem Let A be the number of days that A will take to complete the job alone, B days for B to complete the job alone and C days for C to complete the job alone. A and B can do a job in 6 days. They complete ( 1 6 )th of the job in a day. i.e. 1 A + 1 B = 1 6 ------- -- (1) Similarly, B and C will complete ( 1 10 )th of the job in a day. i.e 1 B + 1 C = 1 10 ---------- (2) And C and A will complete 1 7.5 or ( 2 15 )th of the job in a day i.e 1 C + 1 A = 2 15 ------------ (3). Subtracting eqn (2) from eqn (1) We get 1 A − 1 C = 1 6 − 1 10 = 1 15 ----------- (4) Adding eqn (4) and eqn (3) we get, 1 A − 1 C + 1 A + 1 C = 2 A = 1 15 + 2 15 = 1 5 ⇒ 1 A = 1 10 . i.e. A does 1 10 of the job in a day and therefore, will take 10 days to complete the job working alone.

57.

Anil does a work in 90 days, Bittu in 40 days and Chintu in 12 days. They work one after another for a day each, starting with Anil followed by Bittu and then by Chintu. If the total wages received are Rs 360 and Anil, Bittu, Chintu share them in the ratio of the work done, find their respective individual wages.

 A. Rs 40, Rs 60 and Rs 260 B. Rs 36, Rs 81 and Rs 243 C. Rs 42, Rs 86 and Rs 232 D. Rs 38, Rs 88 and Rs 234
Answer:B
Explanation: Assume there are 360 units of work (LCM of 40,60 and 12). Hence, A,B and C can do 4,9 and 30 units per day or together 43 units every 3 days. So In 24 days, 43×8=344 units of work is completed. In the next 2 days, 13 units are completed and on 27th day, C takes ( 1 10 )th of a day to finish the rest. So, A and B worked for 9 days each and have hence put in 36 and 81 units respectively, and the rest of the 243 units is put in by C. The wages shall also be distributed in the same ratio as: Rs 36, Rs 81 and Rs 243.