Theory of Equations Test

Result

Theory of Equations Test - 1

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Question 1
1 / -0

In a shop, the cost of 3 burgers, 7 milkshakes and French fries is Rs. 120. In the same shop, the cost of 4 burgers, 10 milkshakes and French fries is Rs. 164.5. Find the cost of 1 burger, 1 milkshake and French fries in the shop.

A
Rs. 41

B
Rs. 21

C
Rs. 31

D
Rs. 51

Solution

3B + 7M + F = 120 .……..(1)
4B + 10M + F = 164.5 …….. (2)
(2) – (1)
⇒ B + 3M = 44.5 ……... (3)
2B + 6M = 89
Putting (3) in (1), we get
⇒ (2B + 6M) + B + M + F = 120
⇒ B + M + F = 31
Question 2
1 / -0

A two digit number becomes five-sixth of itself if the digits are reversed. The two digits differ by one. The number is

A
56

B
54

C
45

D
65

Solution

5/6 (10a + b) = 10b + a ……….. (1)

And a - b = 1 ………. (2)
From (1),

50a + 5b = 60b + 6a

⇒ 4a = 5b

or we have
b = 4
a = 5
Question 3
1 / -0

How many positive integer pairs (a, b) satisfy the equation ab = a + b + 20?

A
0

B
2

C
3

D
4

Solution

ab = a + b + 20
ab - a = b - 1 + 21

a(b - 1) - 1 (b - 1) = 21
(a - 1) (b - 1) = 21
= 1 × 21, 3 × 7, 7 × 3, 21 × 1
∴ a = 2, b = 22

a = 4, b = 8
a = 8, b = 4
a = 22, b = 2

Total of 4 pairs satisfy the given equation.
Question 4
1 / -0

The number of solutions of the equation 7x + 3y = 123, where x, y > 0, is

A
3

B
4

C
5

D
6

Solution

7x + 3y = 123
When, y = 6, x = 15
y = 13, x = 12
y = 20, x = 9
y = 27, x = 6
y = 34, x = 3

Here, above solutions are ordered pairs.

So, we have used the concepts of ordered pair.

The only possible pairs when x, y > 0 is 5.
Question 5
1 / -0

A piece of string is 40 cm long. It is cut into three pieces. The longest piece is three times as long as the middle-sized and the shortest piece is 23 cm shorter than the longest piece. Find the length of the shortest piece.

A
27 cm

B
5 cm

C
4 cm

D
9 cm

Solution

Let the largest piece of string be 3x cm, then middle-sized and the shortest piece would be x cm and
(3x - 23) cm,
respectively.
Or 3x + x + (3x - 23) = 40

⇒ x = 9
Therefore, the shortest piece = (3 × 9 - 23) = 4