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Algebra Level 2 Test 1

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Question 1
If the ages of P and R are added to twice the age of Q, the total becomes 59. If the ages of Q and Rare added to thrice the age of P, the total becomes 68 and if the age of P is added to thrice the age of Q and thrice the age of R, the total becomes 108. What is the age of P?
A
17 yr
B
19 yr
C
15 yr
D
12 yr
Question 1 Explanation: 
From the given conditions we can say that 2Q +P +R = 59 …………………………………1 Q + R + 3P = 68…………………………………2 P +3Q +3R = 108……………………………….3 From 2 and 3 3Q + 3R + 9P = 204 P +3Q +3R = 108 So therefore 8P= 96 = P = 12
Question 2
A father's age is three times the sum of the ages of his two children, but 20 yr hence his age will be equal to the sum of their ages. Then, the father's age is
A
30 yr
B
40 yr
C
35 yr
D
45 yr
Question 2 Explanation: 
Let the age of father = p years Let the age of the children = q and r years From the question (q + r) = p/3 And also (q +r )+ 20 +20 = p + 20 On solving for p p = 30 years
Question 3
In a family, the father took ¼ of the cake and he had 3 times as much as others had. The total number of family members is
A
7
B
3
C
10
D
12
Question 3 Explanation: 
Let the number of members other than the father = p Therefore 3/4cake owned by these members Therefore 3/4p x 3 =1/4 p = 9 Therefore the number of members in the family = 10
Question 4
Five engines consume 6 metric tonne of coal when each is running 9 h a day. How much coal (in metric  tonnes) will be needed for 8 engines, each running  10 h a day, it being given that 3 engines of the former type consume as much as 4 engines of the  latter type?
A
6.48
B
31/8
C
8
D
85/9
Question 4 Explanation: 
Let the quantity to be needed= p So from question we can say that (5 x 9)/6 = (8 x 10)/p x ¾ p = {(8 x 10 x 3) / (4 x 5 x 9)} x 6 = 8
Question 5
A body of 7300 troops is formed of 4 battalions so that 1/2 of the first, 2/3 of the second, 3/4 of the third and 4/5 of the fourth are all composed of the same number of men. Find the same number.
A
1250
B
1200
C
1300
D
1350
Question 5 Explanation: 
Number of troops = 7300 Number of battalions = 4 Let battalions are p, q, r, s, respectively So therefore from the question we can say that p/2 = 2q/3 = 3r/4 = 4s/5 Therefore the values will be q = 3/4p r = 2/3p s = 5/8p And also we are given by p + q + r + s = 7300 By putting these all above values p would be = 2400 Therefore same number of men are = 2400/2 = 1200
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