Mock Test-2 (Paper-1) (Question 101-125)

Total Questions: 25

11. If the numerator of a fraction increased by 200% and the denominator of the fraction is increased by 120%, the resultant fraction is 4/11 What is the original fraction?

Correct Answer: (a) 4/15
Solution:Let the original fraction be x/y

According to the question,

(x × 300/100) ÷ (y × 220/100) = 4/11

⇒ 30x/22y = 4/11

⇒ x/y = 4/11 × 22/30 = 4/15

12. The sum of a series of 5 consecutive odd numbers is 195. The second lowest number of this series is 9 less than the second highest number of another series of 5 consecutive even numbers. What is 40% of the second lowest number of the series of consecutive even numbers?

Correct Answer: (a) 16.8
Solution:Five consecutive odd numbers

⇒ x, x + 2 x + 4 x + 6 and x + 8

∴ x + x + 2 + x + 4 + x + 6 + x + 8 = 195

⇒ 5x + 20 = 195

⇒ 5x = 195 - 20 = 175

⇒ x = 175/5 = 35

Second lowest number = 35+2=47

Second highest even number = 37 + 9 = 46

Second lowest even nu dot number = 42

40% of 42 = (42 × 40)/100 = 16.8

13. In every 30 minutes the time of a watch increases by 3 minutes. After setting the correct time at 5 am., what time will the watch show after 6 hours?

Correct Answer: (c) 11:36 a.m.
Solution:Time gained in 6 hours = 12 × 3 = 36 minutes

∴ Required time = 11 : 36 a.m.

14. Ms. Pooja Pushpan invests 13% of her monthly salary, i.e., 8554 in Mediclaim Policies. Later she invests 23% of her monthly salary on Child Education Policies. Also she invests another 8% of her monthly salary on Mutual Funds. What is the total annual amount invested by Ms. Pooja Pushpan?

Correct Answer: (c) ₹347424
Solution:Let Ms. Pooja Pushpan's monthly salary = ₹ x

According to the question, 13% of the x = ₹ 8554

⇒ x = ₹ ((8554 × 100)/13) = ₹ 65800

Total monthly investment in percentage

= 13 + 23 + 8 = 44%

∴ Total monthly investment

= 44% of ₹ 65800 = ₹ ((44 × 65800)/100) = ₹ 28952

∴ Total annual investment

= ₹ (12 × 28952) = ₹ 347424

15. On a 10,000 payment order, a person has choice between 3 successive discounts of 10%, 10%, and 30%, and 3 successive discounts of 40%, 5% and 5%. By choosing the better one he can save (in):

Correct Answer: (b) 255
Solution:Selling price in the first case

= 70% of 90% of 90% of ₹ 10000

= 70/100 × 90/100 × 90/100 × 1000 = ₹ 5670

Selling price in the second case

= 95% of 95% of 60% of ₹ 10000

= 95/100 × 95/100 × 60/100 × 1000 = ₹ 5415

∴ Saving = ₹ (5670 - 5415) = ₹ 255

16. The sum of Shilpa's age after 4 years and Raghu's age 4 years ago is 63 years and the respective ratio between the Shilpa's age four years ago and Raghu's age after 3 years is 10:21. What is Shilpa's present age? (in years)

Correct Answer: (c) 24
Solution:According to the question,

Sum of the present ages of Shilpa and Raghu = 63 years

Shilpa's present age = x years (let)

∴ Raghu's present age = (63 - x) years

Shilpa's age 4 years ago = (x - 4) years

and Raghu's age 3 years hence

= (63 - x + 3) years=(66-x) years

ATQ,

∴ (x - 4)/(66 - x) = 10/21

⇒ 21x - 84 = 660 - 10x

⇒ 21x + 10x = 660 + 84

⇒ 31x = 744

⇒ x = 744/31 = 24 years

17. An amount of money appreciates to ₹7,000 after 4 years and to 10,000 after 8 years at a certain compound interest compounded annually. The initial amount of money was

Correct Answer: (b) ₹4900
Solution:

A₂/A₁ = 10000/7000 = 10/7

Note: Amount will increase in multiple.

∴ P × 10/7 = 7000

∴ P = ₹ 4900

∴ Hence required principal = ₹ 4900

18. Three circles of equal radius 'a' cm touch each other. The area of the shaded region is :

Correct Answer: (d)
Solution:

19. The angle of elevation of the top point of a vertical tower situated perpendicularly on a plane is observed as 60° from a point P on the same plane. from another point Q, 10m vertically above the point P, the angle of depression of the foot of the tower is 30°. The height of the tower is

Correct Answer: (b) 30 m
Solution:

AB = Tower

QP = 10 metre in ΔQBP

tan 30º = (QP)/(PB)

1/√3 = (QP)/(PB)

⇒ QP : PB = 1 : √3 .....(i)

In ΔABP

tan 60º = (AB)/(BP)

20. The points A (-4, -1), B (-2, -4), C (4, 0) and D (2, 3) are the vertices of a

Correct Answer: (b) Rectangle
Solution:length of AB = √(2 ²+ 3²) = √(13)

length of CD = √(2 ²+ 3²) = √(13)

slope of  AB = (- 4 + 1)/(- 2 + 4) = - 3/2

slope of CD = (3 + 0)/(2 - 4) = - 3/2

slope of BC = (0 + 4)/(4 + 2) = 2/3

∵  slope of BC × slope of AB = - 1

AB = CD  ∴  ABCD is rectangle