1. The square of the tens digit of a two-digit number is 7 less than the sum of the digits. If the digits are transposed the number is increased by 63. Find the number.
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1. The square of the tens digit of a two-digit number is 7 less than the sum of the
digits. If the digits are transposed the number is increased by 63. Find the
number.
2. The sum of the digits of a 2-digit number is 10. If the number is divided by the
units digit, the quotient is 3 and the remainder is 4. Find the number.
3. It took a certain vehicle 3 hours to travel a distance of 120 km. On its way
back, it took him only 2 hours in traveling the same path. What was his average
speed?
4. A motorboat can travel 4 km upstream at the same time it can travel 9 km
downstream. If the velocity of the current is 8 kph, find the velocity of the boat in
still water.
5. A gardener can mow a lawn in 3 hours. After 2 hours, it rained and he
discontinued the work. In the afternoon, a girl completed the rest of the work in
1 hour and 15 minutes. How long would it take the girl to mow the lawn alone?
6. John, Paul, and George can finish a job in 12, 16, and 19 hours respectively.
John and Paul worked together for 4 hours. Paul got tired so George worked in
place of him until the job is finished. How long did John work?
7. A man left his home at past 3:00 PM as indicated on his wall clock. Between
two to three hours after, he returned home and noticed that the hands of the
clock interchanged. At what time did he leave his home?
8. A container is filled with 70 liters which are 40% alcohol by volume. How much of
a mixture must be taken and then replaced with an equal amount of water so that
the resulting solution is 30% alcohol by volume?
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