Answer:
Answer:
Answer:
Answer:
Answer:
Answer:
Answer:
Dividing by
Question 8: If the ratio between 8 and 11 is the same as the ratio of , find the value of
Answer:
Question 9: Two numbers are in the ratio 2:3. If 5 is added to each number, the ratio becomes 5:7. Find the numbers.
Answer:
Let the number be . Therefore
Question 10: Two positive numbers are in the ratio of 3:5 and the difference between their squares is 400. Find the numbers.
Answer:
Let the number be
Question 11: What quantity must be subtracted from each term of the ratio 9:17 to make it equal to 1:3.
Answer:
Let be subtracted. Therefore
Question 12: The monthly pocket money of Ravi and Sanjeev is in the ratio of 5:7 Their expenditures are in the ratio of 3:5. If each saves Rs. 80 per month, find their monthly pocket money. [2012]
Answer:
Let monthly pocket of Rave and Sanjeev by respectively.
Substituting
Substituting
Question 13: The work done by men in
days and the work done by
men in
days are in the ratio
. Find the value of
.
Answer:
Question 14: The bus fare between two cities is increased in the ratio of . Find the increase in the fare if: i) the original fare is Rs. 245 and ii) the increased fare is Rs. 207.
Answer:
i)
Therefore Increase in the fare
ii)
Therefore Increase in the fare
Question 15: By increasing the cost of the entry ticket to a fair in the ratio of , the number of visitors to the fair has decreased in the ratio of
. In what ratio has the total collection increased or decreased.
Answer:
Question 16: In a basket, the ratio of the number of oranges and the number of apples is . If 8 oranges and 11 apples are eaten the ratio between the number of oranges and the number of apples becomes
. Find the original number of oranges and apples in the basket.
Answer:
Substituting
Question 17: The ratio between the number of boys and the number of girls in the class is . If there were 20 more boys and 12 less girls, the ratio would have been
. Find the total number of students in the class.
Answer:
… … … … … … … i)
… … … … … … … ii)
Substituting in i)
Hence the total number of students in the class
Question 18: a) If , find
b) If
, find
Answer:
a) … … … … … … … i)
… … … … … … … ii)
Multiplying i) by 6 and ii) by 4 we get
… … … … … … … iii)
… … … … … … … iv)
Hence
b) … … … … … … … i)
… … … … … … … ii)
Multiplying i) by 3 and ii) by 2 we get
… … … … … … … iii)
… … … … … … … iv)
Question 19: If , find
Answer:
… … … … … … … i)
… … … … … … … ii)
Multiplying i) by 6 and ii) by 3 we get
… … … … … … … iii)
… … … … … … … iv)
For question 20 to 29, please refer to the lecture notes on Ratios and Proportions.
Question 20: Find the compound ratio of
i)
ii)
iii)
iv)
Answer:
i)
ii)
iii)
iv)
Question 21: Find duplicate ratio of i) ii)
Answer:
i)
ii)
Question 22: Find triplicate ratio of i) ii)
Answer:
i) Triplicate ratio of
Question 23: Find sub-duplicate ratio of i) ii)
Answer:
i) The sub-duplicate ratio of
i) The sub-duplicate ratio of
Question 24: Find sub triplicate ratio of i) ii)
Answer:
i) The sub-triplicate ratio of
ii) The sub triplicate ratio of
Question 25: Find the reciprocal ratio of i) ii)
Answer:
Question 26: If is the duplicate ratio of
, find
Answer:
Question 27: If is the duplicate ratio of
; show that
Answer:
Hence
Question 28: If is the triplicate ratio of
, find
. [2014]
Answer:
Question 29: Find the ratio compounded of the reciprocal ratio of , the sub – duplicate ration of
and the triplicate ratio of
.
Answer:
Reciprocal Ratio
Sub Duplicate Ratio
Triplicate Ratio
.
Answer: