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. To multiply 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.
18.
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’.
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?
