## TCS Practice Easy Algebra Questions

Dear Reader, in placement papers you may not only expect tough questions but sporadically you can expect simple questions which are easy to answer. You should be shrewd enough to make the most of such questions. This is because you can finish more of these questions in less time.

Question 1

A man raises sheep and chickens. One fine day, his son wants to count the number of sheep and chickens. Farmer gives hit as below :
"The average number of legs for each animal is 2 38/57. There are 19 more chickens than that of sheep." Can you help the son by finding the total number of sheep.

a) 25 b) 19 c)17 d) 20

Solution :

Let the number of sheep be s and the number of chickens be c.

We know every sheep has 4 legs and every chicken has got 2 legs.

Total number of legs = 4s + 2c

Average number of legs = Total number of legs / Total number of all animals

= 4s + 2c / (s + c)

It is given that the average = 2 38/57 = 152/57

Therefore 4s + 2c / (s + c) = 152/57

Or 228s + 114c = 152s + 152c

Or 76s = 38c

Or 2s = c

Also the question states that there are 19 more chickens than that of sheep.

Therefore c - s = 19 ...(1)

Substituting c = 2s in eq 1 we get

2s - s = 19

Or s = 19

Question 2

Ravi had a habit of saving coins given by his mother. He achieved in his objective of saving coins amounting to Rs.50. He had ten 1 rupee coins. The ratio of the number of 25 paise coins to that of 50 paise coins was 10/3. Can you find the number of 25 paise coins he had.

a) 100 b) 105 c) 95 d) 98

Solution :

Let Ravi has X number of 25 paise coins and Y number of 50 paise coins. It is also given that there are ten 1 rupee coins.

Total Rupees he has = Rs. 50.

His total amount in units of paise = 50 x 100 = 5000 paise ...(1)

Amount corresponding to ten 1 rupee coins = 10 x 100 = 1000 paise ...(2)

Amount corresponding to X 25 paise coins = X x 25 = 25X paise ...(3)

Amount corresponding to Y 50 paise coins = Y x 50 = 50Y paise ...(4)

From equations 1,2,3 and 4, Total amount = 1000 + 25X + 50Y = 5000

Or 25X + 50Y = 4000

X + 2Y = 160 ...(5)

Ratio of number of 25 paise coins to that of 50 paise coins = 10/3

i.e X/Y = 10/3

or Y = 3X/10 ...(6)

Substituting eq 6 in eq 5, we get

X + 6X/10 = 160

16X/10 = 160

Or 16X = 1600

Or X = 100

Therefore there are hundred 25 paise coins.

Question 3

Sections A and B of class eight had 20 and 40 students respectively. If the average height of first section was 140 cm and that of the second section was 160 cm, what is the average height of entire class 8 ?

a)154 b) 153.35 c)153.33 d)153.25

Solution :

Average height of students of section A = Total height of all students of section A / Number of students of section A = 140cm

Total height of all students of section A / 20 = 140

Or Total height of all students of section A = 2800

Average height of students of section B = Total height of all students of section B / Number of students of section B = 160cm

Total height of all students of section B / 40 = 160

Or Total height of all students of section B = 6400

Average height of entire class eight

= Total height of all students belonging to both the sections / Total number of students in both the sections put together

= 2800 + 6400 / 20 + 40 = 9200 / 60 = 153.33 cm

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