   Directions: Study the following question carefully and choose the right answer given beside.
Important for :
1
A principal of Rs. 6120 becomes Rs. 8330 in 2 years when compounded annually at some rate of interest. How much will be the amount if the same principal was compounded half-yearly?
» Explain it
A
Now the formula for amount on compound interest basis can be given as

 A = P ( 1 + R ) t 100

Where A = Amount

P = Principal

R = Rate of interest

T= Time period

Now as per our data P = 6120, A = 8330, t = 2 years

 ∴ 8330 = 6120 ( 1 + R ) 2 100

 ∴ 8330 = ( 1 + R ) 2 6120 100

 ∴ 49 = ( 1 + R ) 2 36 100

 ∴ 7 = 1 + R 6 100

 ∴ R = 100 = 16.67% 6

Now the amount when the same principal is compounded half-yearly for the same time period can be given as
 A = 6120 [ 1 + ( 16.67 ) ] 2× 2 200

∴ A = 6120 × 1.377

∴ A = Rs. 8430

Hence, option A is correct.

2
20 men, 12 women and 18 boys were given a project of doing 3960 designs of a building in 5 days. The ratio of the number of designs made by them respectively in 1 day is 3 : 2 : 1. If on the 1st day all of them worked, on the 2nd day 4 women and 6 boys went absent and on the 3rd day, 6 men and 10 boys went absent but still the work got finished on the 3rd day. Then find the number of designs designed by them on the 3rd day?
» Explain it
B
Let the number of designed by men, women and boys in 1 day be 3x, 2x and x respectively.

Designs of building on the 1st day

⇒ 20 × 3x + 12 × 2x + 18 × x

⇒ 102x

On the 2nd day = 20 × 3x + 8 × 2x + 12 × x = 88x

On the 3rd day = 14 × 3x + 12 × 2x + 8 × x = 74x

Now, 102x + 88x + 74x = 3960

⇒ 264x = 3960

 ⇒ 74x = 3960 × 74 264

⇒ 74x = 1110

Hence, option B is correct.

3
Rohit can row a boat 65Km upstream and 130Km downstream in 23 hours, whereas he can swim 45Km upstream and 104Km downstream in 17 hours. Find the speed of boat in still water and the speed of stream.
» Explain it
C
Upstream, U = Speed of boat – speed of stream

Downstream, D = Speed of boat + speed of stream

 65 + 130 = 23 U D

 45 + 104 = 17 U D

On solving the above two equations, we will get

U = Speed of boat – speed of stream = 5

D = Speed of boat + speed of stream = 13

Thus, Speed of boat = 9 and speed of stream = 4

Hence, option C is correct.

4
An exam was conducted in a state over 222 centers. The average number of applicants per centre was found to be 1560. However, it was later realized that in one centre, the number of applicants was counted as 1857 instead of 1747. What was the correct average number of applicants per centre (upto two decimals)?
» Explain it
D
Number of applicants that have been counted extra = 1857 − 1747 = 110

 Hence, decrease in average = 110 = 0.495 222

∴ Correct average = 1560 − 0.495 = 1559.505 = 1559.51

Hence, option D is correct.

5
A chaiwala has 2 types of mixture of tea with him. In 56 kg of first mixture ratio of tea to impurity is 5 : 2 and in 44 kg of second mixture the ratio of tea to impurity is 3 : 1. If he mixes these two mixture with 17 kg of pure tea in a large container, then find the ratio of tea to impurity in the large container.
» Explain it
A
 In 56 kg of first mixture, Tea = 56 × 5 7

= 40 kg and impurity = 56 – 40 = 16 kg
 In 44 kg of second mixture, Tea = 44 × 3 4
= 33 kg and impurity = 44 – 33 = 11 kg

In large container quantity of pure tea = 40 + 33 + 17 = 90 kg

In large container quantity of impurity = 16 + 11 = 27 kg

Required ratio = 90 : 27 = 10 : 3

Hence, option A is correct.

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