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1. The average weight of 13 boys in a class is 57 kg and if a boy walks out of the class the average is decreased by 3/4 kg. What is the weight of the boy who walked out of the class?

2. Ratio of girls to boys in a class in 2016 was 20 : 9 and the ratio of girls to boys in the same class in 2017 is 11 : 9. Find the total number of boys in the class in 2016 if the ratio of total number of students in the class in 2016 to the total number of students in the class in 2017 is 29 : 40 and total number of girls in the class in both the years is 84.

3. A, B and C entered into a partnership such that the initial investment of A is half of C and initial investment of B is 25% less than that of C. A, B and C withdrew Rs.2000, Rs.5000 and Rs.8000 respectively after 4 months, 5 months and 3 months respectively such that at the end of 6 months profit is divided in 56: 85: 96 ratio. Find the sum of initial investment of A, B and C.

4. To promote his movie SRK announces 20% instant cash back on LayTm app booking which otherwise had costed Rs.250. Due to this the sales of the movie tickets increased by 28%. Find the increase in percentage of number of people who have watched the movie.

5. A’s salary is 25% lower than B’s salary, which is 20% lower than C’s salary. D’s salary is 14.28% more than C’s salary. By how much percent (approx.) D’s salary is more than A’s salary?

6. A whole seller mixes three variety of rice costing Rs.40/kg, Rs.48 per kg and Rs.55/kg in the quantity 3 kg, 5 kg and 8 kg respectively. He sells this mixture to a shopkeeper at a profit of 5% and the shopkeeper sells the same mixture to his customer at a profit of 10%. Find the amount paid by customer if he purchases 12 kg rice.

7. A sum of money becomes two times in 8 years at simple interest and it becomes four times in 2 years at compound interest. Find the ratio of rate of simple interest to rate of compound interest –

8. Average age of 8 persons of a team is 22.5 years, out which A is 4 years older to B. 2 years ago the average age of team excluding the age of A and B is 20 years. Find the ratio of ages of A and B respectively after 6 years from present.

9. Harish going in his car from city X to city Y takes eight hours travelling at a speed of 75 kmph, while Mahesh travels the same distance in ten hours. If Harish travelled the distance at a speed of 5 kmph more and Mahesh at 10 kmph less then what would be the difference between the time taken by Mahesh and Harish to cover the distance?

10. A is twice as good as workman as B and together they finish a piece of work in 16 days. In how many days will A alone finish the work ?

**Check your Answers below:**

##### 1. Question

The average weight of 13 boys in a class is 57 kg and if a boy walks out of the class the average is decreased by 3/4 kg. What is the weight of the boy who walked out of the class?

Ans: 2

Let the weight of the boy, who walked out of the class be ‘x’.

So, x = 13*57 – 12*(57-3/4)

The weight of the boy = 13 * 57 – 12 * (57 – 3/4) = 66.##### 2. Question

Ratio of girls to boys in a class in 2016 was 20 : 9 and the ratio of girls to boys in the same class in 2017 is 11 : 9. Find the total number of boys in the class in 2016 if the ratio of total number of students in the class in 2016 to the total number of students in the class in 2017 is 29 : 40 and total number of girls in the class in both the years is 84.

Ans: 4

Let number of girls and boys in 2016 = 20x and 9x respectively.

Let number of girls and boys in 2017 = 11y and 9y respectively.

According to question-

=> (20x + 9x) : (11y + 9y) = 29 : 40

=> 29x : 20y = 29 : 40

=> y = 2x

And,

=> 20x + 11y = 84

=> 20x + 22x = 84

=> x = 2 and y = 4

Total number of boys in the class in 2016 = 9x = 9 * 2 = 18##### 3. Question

A, B and C entered into a partnership such that the initial investment of A is half of C and initial investment of B is 25% less than that of C. A, B and C withdrew Rs.2000, Rs.5000 and Rs.8000 respectively after 4 months, 5 months and 3 months respectively such that at the end of 6 months profit is divided in 56: 85: 96 ratio. Find the sum of initial investment of A, B and C.

Ans: 2

Let initial investment be,

C = 2t

A = t

B = 1.5t

Ratio of profit share after 6 months is,

=> {t*4 + (t – 2000)*2} : {1.5t*5 + (1.5t – 5000)*1} : {2t*3 + (2t – 8000)*3}

=> (6t – 4000) : (9t – 5000) : (12t + 24000)

Now, ratio given = 56: 85: 96

(6t – 4000) /(9t – 5000) = 56/85

85*6t – 56*9t = 85*4000 – 56*5000

6t = 60000

We get,

t = 10000

So,

Investment are,

A = 10000, B = 1.5t = 15000 and C = 2t = 20000

Sum = 10000+15000 + 20000 = Rs.45000##### 4. Question

To promote his movie SRK announces 20% instant cash back on LayTm app booking which otherwise had costed Rs.250. Due to this the sales of the movie tickets increased by 28%. Find the increase in percentage of number of people who have watched the movie.

Ans: 2

=> Let the initial number of people =100

=> Total revenue =100*250= 25000

=> New cost after cash back =80/100*250

=> =200

Since, sales increased by 28%.

=> Thus, now, total revenue =128*25000/100=32000

=> New no. of people who have cash back= 32000/200

=> =160

=> % increase = ((160-100)/100)*100

=> 60%##### 5. Question

A’s salary is 25% lower than B’s salary, which is 20% lower than C’s salary. D’s salary is 14.28% more than C’s salary. By how much percent (approx.) D’s salary is more than A’s salary?

Ans: 3

Let B’s salary be Rs. 100. Then,

A’s salary = (100% – 75%) 100 = Rs. 75

C’s salary = 100/((100%-20%))= Rs. 125

D’s salary = (100% + 14.28%) 125 = 8 * 125 / 7 = Rs. 142.85

Required % = (142.85 – 75)/75 = 90.47%##### 6. Question

A whole seller mixes three variety of rice costing Rs.40/kg, Rs.48 per kg and Rs.55/kg in the quantity 3 kg, 5 kg and 8 kg respectively. He sells this mixture to a shopkeeper at a profit of 5% and the shopkeeper sells the same mixture to his customer at a profit of 10%. Find the amount paid by customer if he purchases 12 kg rice.

Ans: 4

Total quantity of rice mixed = 3 + 5 + 8 = 16 kg

Total cost of mixer = (40 * 3) + (48 * 5) + (55 * 8) = 120 + 240 + 440 = Rs.800

Per kg cost of mixer for whole seller = 800/16 = Rs.50

Per kg cost of mixer for shopkeeper when whole seller made 5% profit = 105% of 50 = Rs.52.5

Per kg cost of mixer for customer when shopkeeper made 10% profit = 110% of 52.5 = Rs.57.75

Total amount paid by customer for 12 kg of this mixture of rice = 57.75 * 12 = Rs.693##### 7. Question

A sum of money becomes two times in 8 years at simple interest and it becomes four times in 2 years at compound interest. Find the ratio of rate of simple interest to rate of compound interest –

Ans: 2

Let principal is P and rate is r1 for simple interest and r2 for compound interest.First Case:-P = (P * r1 * 8)/100

r1 = 12.5%

Second Case:-

4P = P(1 + r2/100)

^{2}r2 = 100%

Ratio = r1:r2 = 12.5:100 =

**1:8**##### 8. Question

Average age of 8 persons of a team is 22.5 years, out which A is 4 years older to B. 2 years ago the average age of team excluding the age of A and B is 20 years. Find the ratio of ages of A and B respectively after 6 years from present.

Ans: 4

Let the present age of B = P years and present age of A = (P + 4) years.

Total age of 8 persons at present = 22.5 * 8 = 180

Average age of 6 persons before 2 years = 20 years. So, average of those 6 persons at present = 20 + 2 = 22 years.

Total age of 6 persons at present = 22 * 6 = 132

Sum of ages of A and B = P + P + 4 = 180 – 132 = 48

=> 2P = 44

=> P = 22

Age of A after 6 years = P + 4 + 6 = 22 + 10 = 32 years

Age of B after 6 years = P + 6 = 22 + 6 = 28 years

Required ratio = 32: 28 = 8: 7##### 9. Question

Harish going in his car from city X to city Y takes eight hours travelling at a speed of 75 kmph, while Mahesh travels the same distance in ten hours. If Harish travelled the distance at a speed of 5 kmph more and Mahesh at 10 kmph less then what would be the difference between the time taken by Mahesh and Harish to cover the distance?

Ans: 1

The distance between cities X and Y = 75 x 8 = 600km.

Speed of Mahesh = 600/10 = 60 kmph

Therefore, the difference between the times taken by Mahesh and

Harish = (600/(60 – 10)) – (600/(75 + 5)) = 4.5 hrs.

Hence the correct option is (1).##### 10. Question

A is twice as good as workman as B and together they finish a piece of work in 16 days. In how many days will A alone finish the work ?

Ans: 2

(A’s 1 day’s work) : (B’s 1 day’s work) = 2 : 1

(A + B)’s 1 day’s work = 1/16

Divide 1/16 in the ratio 2 : 1

Therefore, A’s 1 day’s work = (1/16 * 2/3)

= 1/24

= 24 days

Hence, A alone can finish the work in 24 days