Quick tricks
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* X alone can do 1/20 of the work in 1 day * Y alone can do 1/12 of the work in 1 day * In 4 days, X did 4/20 = 1/5 of the work * The total work is 1 * So the remaining work is 1 - 1/5 = 4/5 * X and Y's daily work is 1/20 + 1/12 = 5/60 * Equating: 4/5 = (Number of days) * (5/60) * Number of days = 20 Therefore, the total number of days to complete the work is 20 days.
Quick tricks
- 2. 1.1 = 1 11 . 11 = 121 111 . 111 = 12321 1111 . 1111 = 1234321 11111 . 11111 = 123454321 111111 . 111111 = 12345654321 1111111 . 1111111 = 1234567654321 11111111 . 11111111 = 123456787654321 111111111 . 111111111 = 12345678987654321
- 3. 12345679 . 9 = 111111111 12345679 . 18 = 222222222 12345679 . 27 = 333333333 12345679 . 36 = 444444444 12345679 . 45 = 555555555 12345679 . 54 = 666666666 12345679 . 63 = 777777777 12345679 . 72 = 888888888 12345679 . 81 = 999999999
- 4. 987654321 . 9 = 08 888 888 889 987654321 . 18 = 17 777 777 778 987654321 . 27 = 26 666 666 667 987654321 . 36 = 35 555 555 556 987654321 . 45 = 44 444 444 445 987654321 . 54 = 53 333 333 334 987654321 . 63 = 62 222 222 223 987654321 . 72 = 71 111 111 112 987654321 . 81 = 80 000 000 001
- 5. 999999 . 1 = 0999999 999999 . 2 = 1999998 999999 . 3 = 2999997 999999 . 4 = 3999996 999999 . 5 = 4999995 999999 . 6 = 5999994 999999 . 7 = 6999993 999999 . 8 = 7999992 999999 . 9 = 8999991 999999 . 10 = 9999990
- 6. 9 . 9 = 81 99 . 99 = 9801 999 . 999 = 998001 9999 . 9999 = 99980001 99999 . 99999 = 9999800001 999999 . 999999 = 999998000001 9999999 . 9999999 = 99999980000001
- 7. 0.9+1=1 1 . 9 + 2 = 11 12 . 9 + 3 = 111 123 . 9 + 4 = 1111 1234 . 9 + 5 = 11111 12345 . 9 + 6 = 111111 123456 . 9 + 7 = 1111111 1234567 . 9 + 8 = 11111111 12345678 . 9 + 9 = 111111111
- 8. 1 .8+1=9 12 . 8 + 2 = 98 123 . 8 + 3 = 987 1234 . 8 + 4 = 9876 12345 . 8 + 5 = 98765 123456 . 8 + 6 = 987654 1234567 . 8 + 7 = 9876543 12345678 . 8 + 8 = 98765432 123456789 . 8 + 9 = 987654321
- 15. Tomultiply by 21: Double the number, then multiply by 10 and add the original number. For example: To multiply 37 by 21, Double 37 yields 74,multiply by 10 to get 740 and then add the original number 37 to get 777.
- 16. Tomultiply by 31: Triple the number, then multiply by 10 and add the original number. For example: To multiply 43 by 31, Triple 43 yields 129,multiply by 10 to get 1,290 and then add the original number 43 to get 1,333.
- 17. Tomultiply by 41: Quadruple the number, then multiply by 10 and add the original number. For example: To multiply 47 by 41, Quadruple 47 yields 188,multiply by 10 to get 1,880 and then add the original number 47 to get 1,927.
- 19. • A number is divisible by ‘2’ if it ends in zero or in a digit which is a multiple of ‘2’i.e. 2,4, 6, 8. • A number is divisible by ‘3’, if the sum of the digits is divisible by ‘3’. • A number is divisible by ‘4’ if the number formed by the last two digits, i.e. tens and units are divisible by 4. • A number is divisible by ‘5’ if it ends in zero or 5. • A number is divisible by ‘6’ if it divisible by ‘2’ and ‘3’. • A number is divisible by ‘8’ if the number formed by the last three digits, is divisible by ‘8’. • A number is divisible by ‘9’ if the sum of its digit is divisible by ‘9’. • A number is divisible by ‘10’ if it ends in zero. • A number is divisible by ‘11’ if the difference between the sums of the digits in the even and odd places is zero or a multiple of ‘11’.
- 20. TIME AND WORK
- 21. • A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is : A. 1/4 B. 1/10 C. 7/15 D. 8/15
- 22. 1. If 12 men can do a piece of work in 36 days. In how many days 18 men can do the same work? 2. A and B can finish a work in 16 days, while A alone can do the same work in 24 days. In how many days, B alone can finish the same work?
- 23. If 6 men dig 100 meters in 20 days working 8 hours, how many men are required to dig 200 meters in 10 days working 4 hours? If 20 men cut 40 trees working 8 hours each day in 10 days. Find out how many trees will be cut by 30 men working 4 hours a day for 20 days?
- 24. • A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
- 25. • P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?
- 26. • X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?