# Quant Test for NIACL 2018 Prelim Exam Set – 5

Directions(1-5): Find the relation between x and y and choose a correct option.

1. I. 8 x^2 + 78 x + 169 = 0
II. 20y^2 – 117 y + 169 = 0

x>y
x>=y
y>x
x=y or relation cannot be established.
y>=x
Option C
x = – 13/4, –13/2
y = 13/5, 13/4 x < y

2. I. 6x^2 – 25 x + 25 = 0
II. 15y^2 – 16 y + 4 = 0

x=y or relation cannot be established.
y>x
x>=y
x>y
y>=x
Option D
x = 10/6, 15/6
y = 6/15, 10/15
x > y

3. I. 6 x + 5 y = 30 xy
II. 5 x + 6 y = 35 xy

y>x
x=y or relation cannot be established.
y>=x
x>y
x>=y
Option A
6x + 5y = 30xy
5x + 6y = 35 xy
6/y+ 5/x = 30] × 6
5/y + 6/ x = 35 ] × 5
x = 11/60, y = 11/5
x < y

4. I. √x + 18 = √144 – √49
II. y^2 + 409 = 473

x>=y
x>y
x=y or relation cannot be established.
y>=x
y>x
Option C
(18x)^1/2 = 5
x + 18 = 25
x = 7 y^2 = 64 y = + 8 No relation

5. I. y^2 – x^2 = 32
II. y – x = 2

x=y or relation cannot be established.
x>=y
x>y
y>x
y>=x
Option D
y – x = 2
y = x + 2
(x + 2)^2 – x^2 = 32
X^2 + 4 + 4x – x^2 = 32
4x = 28
x = 7
y = 9
x < y

6. Directions(6-10):
The following pie-chart shows the percentage distribution of the expenditure incurred in publishing a book. Study the pie-chart and the answer the questions based on it.
Various Expenditures (in percentage) Incurred in Publishing a Book 7. If 5500 copies are published and the transportation cost on them amounts to Rs. 82500, then what should be the selling price of the book so that the publisher can earn a profit of 25%?
Rs. 187.50
Rs. 100.15
Rs. 124.32
Rs. 111.25
Rs. 107.15
Option A
For the publisher to earn a profit of 25%,
S.P. = 125% of C.P. Transportation Cost = 10% of C.P Let the S.P. of 5500 books be Rs. x.
Then, 10 : 125 = 82500 : x.
x = Rs. [(125 x 82500) x 10] = Rs. 1031250 S.P. of one book = Rs. (1031250/ 5500)
= Rs. 187.50

8. What % Royalty on the book is less than the printing cost?
40%
25%
15%
30%
20%
Option B
Printing Cost of book = 20% of C.P.
Royalty on book = 15% of C.P. Difference = (20% of C.P.) – (15% of C.P)
= 5% of C.P.
Percentage difference = (Difference/Printing) * 100% = [ ( 5% of C.P./Printing Cost ) x 100%] = 25%

9. The price of the book is marked 20% above the C.P. If the marked price of the book is Rs 180 , then what is the cost of the paper used in a single copy of the book?
Rs. 33. 15
Rs. 25. 10
Rs. 30. 21
Rs. 28. 82
Rs. 37. 50
Option E
Marked price of the book = 120% of C.P.
Also, cost of paper = 25% of C.P
Let the cost of paper for a single book be Rs. x.
Then, 120 : 25 = 180 : x
x = Rs. 37. 50

10. What is the central angle of the sector corresponding to the expenditure incurred on Royalty ?
55
35
40
48
54
Option E
Central angle corresponding to Royalty
= (15% of 360)º
= [(15/100) *360] = 54

11. If for a certain quantity of books, the publisher has to pay Rs. 30,600 as printing cost, and then what will be amount of royalty to be paid for these books?
Rs. 20,150
Rs. 22,950
Rs. 30,000
Rs. 18,950
Rs. 25,500
Option B
Let the amount of Royalty to be paid for these books be Rs. r.
Then, 20 : 15 = 30600 : r
r = Rs. 22,950