1. Sea water contains 5% salt by weight. How many kg of fresh water must be added to 40 kg of sea water for the salt content of the solution to be 2%?

Ans:1
There is 5% of salt in 40 kg of sea water
So, amount of salt in 40 kg of sea water is = 5/100 * 100 = 2 kg
Let the amount of fresh water need to be added be x kg
2kg/(40+x)kg = 2% = 2/100
100 = 40 + x
X = 60kg

 

2. The breadth of a rectangle is three-fourth of its length. The area of rectangle is 1728m2. Find the perimeter of the rectangle?

Ans:5
Let length = ‘L’
Breath = ‘B’ = 3L/4
Area = L*B
= L*3L/4
= 3L2/4
= 1728
L2 = 2304
L = 48 and B = 36
Perimeter = 2(L+B) = 168m

 

3. Present ages of SRK and Akshay are in the ratio of 6:5. After 4 years, the ratio of their ages become 10:9 respectively. Calculate the present age of SRK?

Ans:1
Let SRKs age be 6x and Akshays age be 5x,
(6x+4)/(5x+4) = 10/9
54x + 36 = 50x + 40
=> x = 1
=> SRK’s age = 6*1= 6 years.

 

4. Pawan and Arun started a business with an initial investment of Rs.5000 and Rs.4500 respectively. Pawan adds Rs.250 after 6 months while Arun adds Rs.500 after every 4 months. They used their amount of profit received from the first business at the end of 1 year to start another business. If the ratio of profit from the second business is 41 : 36, then find the ratio of time for which they invested their capital in second business?

Ans:2
Ratio of profit from the first business = (5000 * 6 + 5250 * 6) : (4500 * 4 + 5000 * 4 + 5500 * 4)
=> 61500 : 60000 = 41 : 40
In second business:
Let the amount invested by Pawan be 41x for a time period of T1
Let the amount invested by Arun be 40x for a time period of T2
Ratio of profit from second business = (41x * T1): (40x * T2) = 41: 36
(41x * T1)/ (40x * T2) = 41/ 36
T1/T2 = 10/9
Required ratio = T1: T2 = 10 : 9

 

5. In a competitive exam, the minimum passing percentages for XL and Unreserved are 25% and 45% respectively. An Unreserved candidate scored 83 marks and failed by 25 marks. What is the minimum passing marks for XL?

Ans:3
Passing marks for the Unreserved category = 83 + 25 = 108
∴ 45% of the total marks = 108
=> Total marks = 108/0.45 = 240
∴ Passing marks for XL category = 0.25 * 240 = 60

 

6. A book was sold for Rs. 276 with a profit of 15 %. If it were sold for Rs. 255, then what would have been the percentage profit or loss?

Ans:1
Given, S.P. = Rs. 276 and the Profit = 15%
So, C.P. = 276/1.15 = Rs. 240
When S.P. = Rs. 255,
Profit = Rs. 255 – Rs. 240 = Rs. 15
Therefore, Profit % = (15/240 * 100)% = 6.25%

 

7. Calculate the percentage decrease in consumption of an article if the price is increased by 20% and expenditure is kept same.

Ans:1
Let price = 100
Consumption = 100
New price = 120
New Consumption = x
100*100 = 120*x
x = 100*100/120
250/3
Percentage decrease = (100-250/3)/100 * 100 = 50/300 * 100 = 50/3%
SHORTCUT
Percentage decrease in consumption = (a/(100+a))*100
a = 20%
Percentage decrease in consumption = 20/120 * 100 = 50/3%

 

8. Total interest received from a sum of Rs.12250 at the end of 4 years at certain rate of simple interest is Rs.840 more than the interest received from another sum of Rs.21000 at the end of 2 years at the same rate of simple interest. Find the rate of interest.

Ans:1
Let the interest = R%
Interest received from first sum = (12250 * R * 4)/100 = 490R
Interest received from second sum = (21000 * R * 2)/100 = 420R
According to question-
=> 490R – 420R = 840
=> 70R = 840
=> R = 12%

 

9. A boat takes 12 minutes to row a distance of 10km upstream and it takes 6 minutes to row the same distance downstream. Calculate the speed of boat in still water.

Ans:2
Speed of boat upstream in km/h = 10/12 * 60 = 50 km/h
Speed of boat downstream in km/h = 10/6 * 60 = 100 km/h
Speed of boat in still water = (50 + 100) /2 = 75 Km/h

 

10. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. How many days B alone will take to finish the work?

Ans:1
Let’s suppose A takes 6n days to finish the work hence B will take 3n days and C will take 2n days to finish the work.
Let’s suppose total work = 1 unit
Hence; 1/6n+1/2n+1/3n=1/2
=> 1/n=1/2
=> n = 2
Hence time taken by B = 3n days = 6 days

 

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