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Directions: Study the following question carefully and choose the right answer given beside.
1
If the difference between the compound interest (compounded annually) and the simple interest accrued in one and a half years at 8% per annum is Rs. 80. What is the simple interest in three years on the same amount and at the same rate of interest? 
» Explain it
E
Then CI of one and a half year

[ P  ( 1 +  8 ) 1  ( 1 +  8   ) 1  – p ] ..........(i)
100    2×100  

SI of one and a half year
= P × 3 ×  8   ...........(ii)
 2×100

According to the question, CI – SI = 80

Equation (i) – equation (ii) = 80

By solving, P = 25000

Time = 3 years and Rate of interest = 8% per annum
 
Therefore SI = 25000 × 3 ×  8  = Rs. 6000
100

Alternate method: CI of one and a half year
= 8 + 4 + 8 ×  4  = 12.32%
100

SI of one and a half year = 8 + 4 = 12%

According to the question, (12.32 – 12) % = 80

1% = 250

SI of 3 years = 8 × 4 = 24% = 250 × 24 = Rs. 6000

Hence, option E is correct.
 
2
4 Men can complete a piece of work in 58 days. They started the work together but at the end of every 5th day one man leaves the work and in the place of the man, one woman joins the work and the women continue doing the work and finish it despite all the men left in the mid of the work. Find the total number of days they take to complete the work in this manner if the efficiency of one women is 25% of the efficiency of one man.
» Explain it
B
Total work = 4 × 58 = 232 units (let the efficiency of one man is 1 unit)

Total work was done in the first 5 days

= 5 × 4 = 20 units =  80  units
4
 


Now 3 men and one woman will work in the next five days = efficiency of 3m + 1w

= 3 +  1  =  13
4 4

Total work was done in the second 5 days
= 13 ×  5  =  65  units
4 4

Total work was done in the third 5 days = 2m + 2w
= 2 +  1  = 5 ×  5  =  25  =  50  units
2 2 2 4

Total work was done in the fourth 5 days = 1m + 3w
= 1 +  3  =  7  = 7 ×  5  =  35  units
4 4 4 4
 


After the fourth, 5 days only women will work therefore the total units of work done in the first four, five days = 20 days

80  +  65  +  50  +  35  =  230  units
4 4 4 4 4

Remaining work = 232 –  230  =  698  = 174.5 units
4 4

Efficiency of 4 women = 1 ×  4  = 1 unit
4
 

The number of days taken by 4 women to do 174.5 units = 174.5 days

Total number of days = 174.5 + 20 = 194.5 days

Hence, option B is correct.

3
In a maths test, Anil got 414 marks which was 47 less than Barun’s marks. The marks of Chandan were 48% of the sum of Anil and Barun’s marks together or 52.5% of the total marks. If the marks of Dinesh was 32 more than that of Chandan’s marks. Find how much percent did Dinesh get in that examination? 
» Explain it
E
Barun’s marks = 414 + 47 = 461
 
The sum of Anil’s and Barun's marks = 414 + 461 = 875 
 
Chandan Marks = 48% of 875 = 420 = 52.5% of the total marks = 52.5% of x (let the total marks is x )
 
By solving, x = total marks = 800 
 
Dinesh’s marks = 420 + 32 = 452 
 
Reqd. % =  452 × 100  = 56.5%
800

Hence, option E is correct.

4
The respective ratio of the present age of grandfather, father, mother and son is 25 : 14 : 11 : 6. Before 9 years, the ratio of the age of Grandfather and son was 13 : 3 respectively. What will be the average of the age of father and mother after 9 years?
» Explain it
D
The respective ratio of the present age of grandfather, father, mother and son is 25 : 14 : 11 : 6
 
The ratio of the present age of grandfather and son = 25 : 6

Let us assume it 25x and 6x

According to the question,

25x – 9  =  13
6x – 9 3


By solving, x = 30

The age of father + mother = 14x + 11x = 25x = 25 × 30 = 750

After 9 years, the sum of their age = 750 + 18 = 768 years

Average =  768  = 384 years
2

Hence, option D is correct.

5
If the length of a rectangle is increased by 25% and the breadth is reduced by 33.33% then what will be the effect on its diagonal(approximately)?
» Explain it
A
Let the length of the rectangle = 4 units

And breadth of the rectangle = 3 units

Then diagonal of the rectangle = √(42 + 32) = 5 units

According to the question, the length of a rectangle is increased by 25% and the breadth is reduced by 33.33%

New length = 125% of 4 units = 5 units

New breadth = 66.66% of 3 units = 2 units

In the new rectangle, New diagonal= √(52 + 22) = √29 = approximately 5.38 units

Change = (5.38 – 5) ×  100  = 7.6%
5

Hence, option A is correct.