ALGEBRA ( WORDED PROBLEMS)
1.) Twice the sum of two numbers is 28. The sum of the squares of the two numbers is 100. The
product of two numbers is.
a.) 48 b.) 12 c.) 24 d.) 36
2.) The sum of two numbers is 18 and their difference is 6. Find the smallest number.
a.) 3 b.) 4 c.) 5 d.) 6
3.) The square of a number increased by 16 is the same as 10 times the number. Find the numbers.
a.) 4 & 8 b.) 2 & 8 c.) 6 & 12 d.) 2 & 4
4.) The sum of three consecutive odd integers is 21. What is the first integer?
a.) 2 b.) 4 c.) 5 d.) 8
5.) In four hours, a light plane having air speed of 200 kph flies for 480 km against the wind and
halfway back with same wind. What is the wind speed?
a.) 70 kph b.) 80 kph c.) 90 kph d.) 40 kph
6.) With a tail wind, a plane traveled 120 km in 2 hrs., but the return trip against the same wind took
0.5 hr longer. Find the speed wind.
a.) 54 kph b.) 30 kph c.) 6 kph d.) 40 kph
7.) Jim can travel the 9.5 km from downtown to his home either by riding a bus for 30 minutes and
walking for 20 minutes, or by riding for 10 minutes and walking for 1 hour and 10 minutes. Find
the average rate of walking in kph.
a.) 15 b.) 12 c.) 10 d.) 6
8.) The sum of a number and 8 times its reciprocal is 6. Find the number.
a.) 4 b.) 5 c.) 6 d.) 7
9.) The sum of the digits of a three-digit number is 14. If the hundreds digit is one more than the
tens digit, and the ones digit is three times the hundreds digit. Find the number
a.) 329 b.) 293 c.) 932 d.) 392
10.) In a certain two-digit number, the tens digit exceeds the units digit by 2. If the sum of twice the
original number and three times the number obtained by reversing the digits of the original
number is 321, what is the original number?
a.) 60 b.) 65 c.) 70 d.) 75
11.) A rope 70 m long is cut into two pieces where one is 10 m longer than the other. Find the length
of the longest part.
a.) 10 m b.) 30 m c.) 40 m d.) 70 m
12.) A man owns two square lots of unequal size, together containing 15,025 ft2, if the lots were
contiguous, it would require 530 ft of fence to embrace them in a single enclosure of six sides.
Find the area of the smallest lot.
a.) 625 ft2 b.) 14,625 ft2 c.) 525 ft2 d.) 12,345 ft2
13.) The perimeter of a small rectangular lot is 140 m and its diagonal is 50 m. find the lot area in m 2.
a.) 1200 b.) 1500 c.) 1700 d.) 20,000
14.) How many grams of nickel must be removed from 1500 grams of alloy having 5 % nickel to make
an alloy having 2% nickel?
a.) 45 g b.) 46 g c.) 47 g d.) 48 g
15.) 2000 kg of steel containing 8% nickel is to be made by mixing a steel containing 14% nickel with
another containing 6% nickel. How much of each is needed?
a.) 1000 & 1000 b.) 1500 & 500 c.) 200 & 1800 d.) 1200 & 800
16.) A radiator contains 8L of a 40% antifreeze solution. How many liters of pure antifreeze must be
added to obtain a 50% solution?
a.) 1.6 b.) 1.8 c.) 2 d.) 2.2
17.) What time between three and four 0clock will the hands of the clock be together?
a.) 3:14.36 b.) 3:16.36 c.) 3:18.36 d.) 3:20.36
18.) What time after 7 oclock will the hands of the clock be perpendicular to each other for the first
time?
a.) 7:21.82 b.) 7:19.62 c.) 7:23.75 d.) 7:25.15
19.) What time after one oclock will the hands of the clock be 100 degrees to each other for the first
time?
a.) 1:19.67 b. 1:21.54 c.) 1:23.63 d.) 1:25.63
20.) The sum of the volume and surface area of a cube equals six times the sum of the lengths of its
edges. How long are edges?
a.) 2 b.) 4 c.) 6 d.) 8
