**Dear Aspirants,** **Our SSC Crackers team** is providing a new series of Quantitative Aptitude Questions for **Upcoming Exam **so the aspirants can practice it on a daily basis. These questions are framed by our skilled experts after understanding your needs thoroughly. Aspirants can practice these new series questions daily to familiarize with the exact exam pattern and make your preparation effective.

**1) **

a) 17/13

b) 13/17

c) 13/7

d) 17/7

**2) The sum of two numbers is 25 and sum of their square is 313. Calculate the numbers.**

a) 15, 10

b) 18, 7

c) 11, 14

d) 12, 13

**3) What is the value of a – b when a² + b² – 6a – 6b + 18 = 0 ?**

a) 0

b) 3

c) 6

d) 9

**4) The equation (1+a²) x² + 2abx + (b² – c²) = 0 has equal roots. What is the value of c² (1+a²) ?**

a) a²

b) b²

c) c²

d) ab

**5) A circle of diameter 26 cm having the two equal chords of length 10 cm is separated by a distance x cm. Calculate the distance x.**

a) 20

b) 22

c) 24

d) 28

**6) Two tangents PA and PB are drawn to a circle of centre O in such a way that ****∠****AOB = 120°. Calculate the value of ****∠****APB.**

a) 40°

b) 50°

c) 60°

d) 80°

**7) The population of a town is 200000. It increases annually at the rate of 10%. What will be the population after 2 years?**

a) 240000

b) 242000

c) 221000

d) 244000

**8) The incomes of X and Y are in the ratio 5 : 6 and their expenditure are in the ratio 6 : 5. If X saves Rs 7000 and Y saves Rs 15000, then what will be the income (in Rs) of X?**

a) 28000

b) 20000

c) 25000

d) 24000

**9) X starts a business with Rs 80000. After 6 months Y joins X with Rs 100000. After 2 years, what will be the ratio of proﬁt of X and Y?**

a) 16 : 15

b) 4 : 5

c) 8 : 9

d) 14 : 15

**10) What is the average of all the one digit and two digit natural numbers?**

a) 25

b) 40

c) 50

d) 99

**Answers :**

**1) Answer: A **

**2) Answer: D **

Let the numbers, a & 25 – a

ATQ,

⇒ a² + (25–a)² = 313

⇒a² + 625 + a² – 50a = 313

⇒ 2a² – 50a + 312 = 0

⇒ a²– 25a + 156 = 0

⇒ a²– 13a – 12a+ 156 = 0

⇒a (a–13)–12 (a–13) = 0

⇒ (a–12)(a–13) = 0

a = 13, 12

Required number are, a = 12 or 13 & 25–a = 12

Numbers are 12 and 13.

**3) Answer: A **

a² + b² – 6a – 6b + 18 = 0

a² – 6a + 9 + b² – 6b + 9 = 0

(a–3)² + (b–3)² = 0

⇒ a = 3 & b = 3

⇒ a – b = 3 – 3 = 0

**4) Answer: B **

We have,

(1+a²) x² + 2abx + (b²–c²) = 0

for equal roots

⇒ B² – 4AC = 0

⇒ 4a²b² –4(1+a²) (b²–c²) = 0

⇒4a²b² – 4b² – 4a²b² + 4c² + 4a²c² = 0

⇒ 4c² (1+a²) = 4b²

⇒ c² (1+a²) = b²

**5) Answer: C **

We have, PB = 5cm, OB = 13 cm

∴ OP = 12 cm

Similarly, OQ = 12cm

x = 12 + 12 = 24 cm

**6) Answer: C **

Quadrilateral AOBP,

∠ PAO + ∠AOB + ∠OBP + ∠ APB = 360°

90° + 120° + 90° + ∠ APB = 360°

⇒∠APB = 60°

**7) Answer: B **

**8) Answer: C **

**9) Answer: A **

Profit ratio = Investment ×time

X : Y = 80,000 × 2 : 100000 × 3/2

= 16 : 15

**10) Answer: C **