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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%?

2. The breadth of a rectangle is three-fourth of its length. The area of rectangle is 1728m^{2}. Find the perimeter of the rectangle?

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?

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?

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?

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?

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

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.

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.

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?

**Check your Answers below:**

##### 1. Question

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. Question

The breadth of a rectangle is three-fourth of its length. The area of rectangle is 1728m

^{2}. 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. Question

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. Question

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. Question

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. Question

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. Question

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. Question

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. Question

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. Question

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