Ratios, Averages, Mixtures Home Work

1. A shop keeper uses a balance which has pans whose weights are in the ratio 3:2. A certain quantity of food grains weighs 9 kg when kept in one pan but weighs 8 kg when kept in other pan. Find the actual weight of the food grains.
a. 8.75 kg
b. 8.25 kg
c. 9 kg
d. 8.5 kg

2. A certain number of chocolates were distributed among a few boys who were standing in a row. The second boy got twice as many chocolates as the first boy. The third boy got thrice as many chocolates as the first boy and so on. After the chocolates were distributed completely, the last four boys left the row and their chocolates were distributed among the remaining boys in the same ratio as before. The remaining boys finally have thrice as many chocolates as they got initially. How many boys were there initially?
a. 12
b. 11
c. 9
d. 8

3. Divide Rs.600 among A, B and C So that Rs 40 more than 2/5 th of A’s share, Rs.20 more than 2/7 th of B’s share and Rs.10 more than 9/17 th of C’s share may all be equal. What is A’s share ?
a. Rs 280
b. Rs 150
c. Rs 170
d. Rs 200

4. A box contains a certain number of red, green and blue balls. The number of balls of each colour is more than one. The ratio of the number of red balls to the number of green balls is the same as the ratio of the number green balls to the number of blue balls. If the total number of balls in the box is 61, how may green balls are there in the box?
a. 16
b. 20
c. 25
d. Cannot be determined

5. If the number of balls in the box are 63, then the Number of green balls are number of balls in the box can be (Use data from Question 4)
a. 15
b. 18
c. 20
d. Cannot be determined uniquely

6. In a triangle where all the angles are acute angles, nine times the largest angle is equal to fourteen times the smallest angle. Find the measure of the second largest angle in the triangle of all the angles are integers.
a. 65
b. 54
c. 45
d. 60

7. Peter and Meter are two friends. The sum of their ages is 35 years. Peter is twice as old as Meter was when peter was as old as Meter is now. What is the present age of Peter?
a. 26
b. 22
c. 20
d. 18

8. When Arthur is as old as his father Hailey is now, he shall be 5 times as old as his brother Clarke is now. By then, Clarke will be 8 times older than Arthur is now. The combined ages of Hailey and Arthur are 85 years. How old is Clarke?
a. 12
b. 15
c. 17
d. 20

9. A Father, son and grandson are walking in the park. A man approaches them and asks for their age. The Father replies, "My son is as many weeks as my grandson is in days, and my grandson is as many months old as I am in years. We are all 100 years together. Find the age of the son.
a. 5
b. 8
c. 10
d. 15

10. The average age of Kapil’s family (including his wife and himself) immediately after he had his first child was 14 years. The average age of the family immediately after the birth of the second, third and fourth children was 12, 12 and 15 years respectively. If the average age of Kapil and his wife when they got married was 18 years, then find the number of years after their marriage that their second child was born.
a. 3
b. 4
c. 5
d. 6

11. If the average age of the family today is 18 years, then find the age of the eldest child. (Use data from Question 10)
a. 9 years
b. 10 years
c. 12 years
d. 14 years

12. There are a certain number of pages in a book. Arjun tore a certain page out of the book and later found that the average of the remaining page numbers is \(46\dfrac{{10}}{{13}}\) Which of the following were the page number of the page that Arjun had torn?
a. 57 and 58
b. 59 and 60
c. 45 and 46
d. 47 and 48

13. In the above question, what was the original number of pages in the book? (Use data from Question 12)
a. 94
b. 93
c. 92
d. None of these

14. Geeta wrote the first few natural numbers in her book but happened to miss out one of the numbers. She later calculated the sum of all the numbers that she wrote and divided it by what she thought was the number of numbers she had written. If the result she thus obtained was \(43\dfrac{{7}}{{11}}\), find the number that she forgot to write.
a. 73
b. 17
c. 76
d. 19