# Exercise 9

^{2}+ x – 3 < 0?

^{3}⁄

_{2}< x < 1

(b) -1 < x <

^{3}⁄

_{2}

(c) x > 1

(d) x < -

^{2}⁄

_{5}

(e) None of these

**Ans.a**

2x^{2} + x – 3 < 0

⇒ (x – 1)(2x + 3) < 0 or, -^{3}⁄_{2} < x < 1

(b) 18

(c) 30

(d) Cannot be determined

(e) None of these

**Ans.d**

Let the no. be x.

Then, x - ^{x}⁄_{3} = ^{2}⁄_{3}x

or, ^{2}⁄_{3}x = ^{2}⁄_{3}x

So, can’t be determined is the correct choice.

(b) 13

(c) 19

(d) Cannot be determined

(e) None of these

**Ans.b**

Let the cost of a pen and a pencil be ‘x’ and ‘y’ respectively. We have to find (x – y).

From the question,

2x + 3y = 86 ..... (i)

4x + y = 112 ......(ii)

Subtracting (i) from (ii), we get

2x – 2y = 26 or, x – y = 13

(b) 6

(c) 3

(d) Cannot be determined

(e) None of these

**Ans.a**

Let the two-digit no. be l0x + y.

Then, (10x + y) – (10y + x) = 36

or, 9(x – y) = 36

or, x – y = 4

(b) Sum of the digits is a two-digit number.

(c) Digit in the unit’s place is half of the digit in the ten’s place.

(d) Digit in the unit’s place is twice the digit in the ten’s place.

(e) None of these

**Ans.d**

Suppose the two-digit number is

10 x + y

Then, 10 y + x = 20x + ^{y}⁄_{2}

or 20y + 2x = 40x + y or, y = 2x

^{2}= 12A + 96 and B

^{2}= 2B + 3, then which of the following is the value of 5A + 7B ?

(b) 41

(c) 36

(d) 43

(e) 27

**Ans.b**

9A^{2} = 12A + 96 ⇒ 3A^{2} – 4A – 32 = 0

\ A = \(\frac{4 \pm \sqrt{16 + 384}}{6}\) = 4 , -^{8}⁄_{3}

B^{2} = 2B + 3 ⇒ B^{2} – 2B – 3 = 0

\ B = \(\frac{2 \pm \sqrt{4 + 12}}{2}\) = 3 , -1

\ 5A + 7B = 5 × 4 + 7 × 3 = 20 + 21 = 41

(b) 2680

(c) 2750

(d) 2400

(e) None of these

**Ans.e**

Let the original number of sweets be x.

According to the question,

^{x}⁄_{140} - ^{x}⁄_{175} = 4

or, 175x – 140x = 4 × 140 × 175

or, x = \(\frac{4 \times 140 \times 175}{35} = 2800\)

(b) 24

(c) 48

(d) Data inadequate

(e) None of these

**Ans.a**

Let the two-digit number be l0 x + y.

10x + y = 7(x + y) Þ x = 2y...(i)

10(x + 2) + y + 2 = 6(x + y + 4) +4

or 10x + y + 22 = 6x + 6y + 28 Þ 4x – 5y = 6 ... (ii)

Solving equations (i) and (ii), we get x = 4 and y = 2

(b) 50000

(c) 90000

(d) 30000

(e) None of these

**Ans.a**

Ratio of Ramani’s savings in NSC and PPF = 3: 2

His savings in PPF = ^{2}⁄_{5} × 150000 = 60000

^{1}⁄

_{5}of a number is equal to

^{5}⁄

_{8}of the second number. If 35 is added to the first number then it becomes 4 times of second number. What is the value of the second number?

(b) 70

(c) 40

(d) 25

(e) None of these

**Ans.c**

Let x be the first number and y be the second number.

^{1}⁄_{5}x = ^{5}⁄_{8}y

\ ^{x}⁄_{y} = ^{25}⁄_{8}......(i)

x + 35 = 4y

or, ^{25}⁄_{8}y + 35 = 4y

\ y = 40