SAT (Stage-1) Mock Test

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SAT (Stage-1) Mock Test - 24

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Question 1
1 / -0

The salary of B is 10% more than the salary of A, the salary of C is 10% more than the salary of B, and the salary of D is 10% more than the salary of C. The total salary of A and D is Rs. 2100 more than that of B and C. What is the salary of B?

A
Rs. 1,00,000

B
Rs. 1,10,000

C
Rs. 1,11,000

D
Rs. 1,01,000

Solution

Let salary of A be x.
Then:
Salary of B = 1.1x
Salary of C = 1.21x
Salary of D = 1.331x
A + D = 2.331x
B + C = 2.31x

According to the question:
(A + D) - (B + C) = 2100
0.021x = 2100
x = 1,00,000
Therefore, salary of B is Rs. 1,10,000.
Question 2
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On dividing x⁴ + 2x² - 3x + 7 by a polynomial g(x), the quotient and the remainder were x² + 5 and -3x + 22, respectively. The polynomial g(x) was

A
x - 3

B
x² - 3

C
x² + 3

D
x + 3

Solution

x⁴ + 2x² - 3x + 7 = (x² + 5)g(x) - 3x + 22
Let g(x) = x² + ax + b
Thus, x⁴ + 2x² - 3x + 7 = (x² + 5)(x² + ax + b) - 3x + 22
Or, x⁴+ 2x² - 3x + 7 = x⁴ + ax³+ bx² + 5x² + 5ax + 5b - 3x + 22
Or, x⁴ + 2x² - 3x + 7 = x⁴ + ax³ + x²(b + 5) + x(5a - 3) + 5b + 22
On comparing coefficients, we get
a = 0, b + 5 = 2 or b = -3
Thus, g(x) = x² - 3
Question 3
1 / -0

A tradesman marks an article at a price which would give him a profit of 20% on the cost price. To the favoured customers, he makes a deduction of 5% from the marked price. What actual profit does he receive from the sale of an article to a favoured customer for which the latter pays him $28.50?

A
$3.50

B
$5.70

C
$5.00

D
$5.75

Solution

Let the CP of the article be $x.
MP = x + 20% of x = $1.2x
When a discount is given on this MP,
SP of the article = (95/100) × 1.2x = $1.14x
But 1.14x = 28.50
So, x = 25
CP of the article = $25
SP = $28.50
Profit = $3.50