Govt exams: Learn to tackle problems related to ratio and average

This article is in continuation to the last article on arithmetic that will aid you in your preparation for government recruitment exams. Here are some model questions along with solutions on the Average topic.

When the relation between numbers is given

1. Out of 4 numbers whose average is 60, the first number is one-fourth of the sum of the last three. The first number is?
a) 60 b) 45 c) 48 d) 5
Ans: c
Solution: a = 1/4 (b c d)
a: (b c d) = 1 : 4
5 ->; 240
1 ->; ?
a = 48

2) Of the three numbers whose average is 60, the first number is one-fourth of the sum of the others. The first number is?
a) 42 b) 45 c) 30 d) 36
Ans: d
Solution: a = 1/4 (b c)
a: (b c) = 1 : 4
5 ->; 180
1 ->; ?
a = 36

3) Of the three numbers, the first number is twice the second and the second is thrice the third. If their average is 100, the largest of three is
a) 300 b) 180 c) 150 d) 120
Ans: b
Solution: a = 2b, b = 3c
a: b = 2 : 1, =>; a : b = 6 : 3
b: c = 3 : 1 =>; b : c = 3 : 1
a: b : c = 6 : 3 : 1
10 parts ->; 300
1 part ->; 30
Largest number = 30 × 6 = 180

4) Out of four numbers, the average of first three numbers is thrice the fourth number. If the average of the four numbers is 5, the fourth number is?
a) 2 b) 4 c) 5 d) 4.5
Ans: a
Solution: a b c/ 3 = 3d =>; a b c/ d = 9/1
(a b c): d = 9: 1
10 parts ->; 20
1 part ->; 2
d = 2 × 1 = 2

5) Among three numbers, the first number is twice the second and thrice the third. If the average of the three numbers is 49.5, then the difference between the first and the third number is?
a) 41.5 b) 39.5 c) 54 d) 28
Ans: c
Solution: a/6 = 2b/6 = 3c/6 ( LCM of 2, 3 = 6)
a/6 = b/3 = c/2
a : b : c = 6 : 3 : 2
11 parts ->; 49.5 × 3 = 148.5
4 parts ->; ?
13.5 × 4 = 54

MODEL: Alligations

Alligation is a rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of desired price.

1) The average salary of all the workers in a shop is Rs 8000. The average salary of the 9 technicians is Rs 12000 and the average salary of the rest is Rs 6500. The total number of workers in the workshop is?
a) 31 b) 34 c) 33 d) 32
Ans: c
Solution: Technicians Non-technicians
9 x
12000 6500
8000
1500 4000
9: x = 3 : 8
3x = 9 × 8 =>; x = 24
Total number of workers = 9 24 = 33.

2) Geeta has twice as much money as Rita. Rita has 50 per cent more money than Sita. If the average money of all of them is Rs 220, then the money which Geeta has is?
a) Rs 120 b) Rs 110 c) Rs 180 d) Rs 360
Ans: d
Solution: G = 2R, R = S 50% of S
G : R : S
300% of S : 150% of S : S
300% of S : 150% of S : 100% of S
6 : 3 : 2
11 parts ->; 220 × 3
1 part ->; 60
Geeta = 6 × 60 = 360

To be continued
M.Venkat
Director
MVK Publications
Dilsukhnagar
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