In a college, the students in Science and Commerce faculties were in the ratio of 9 : 7, respectively. If 9 more students joined the Science faculty and 6 students left the Commerce faculty, the ratio of students in the Science and Commerce faculties becomes 12 : 5, respectively. How many students were there in both faculties together initially?
48
Since the initial ratio is 9 : 7, let the initial numbers of students be 9k in Science and 7k in Commerce, where k is a positive whole number.
After 9 students join Science and 6 students leave Commerce, the numbers become 9k + 9 and 7k – 6, and their ratio is 12 : 5, so \(\frac{9k + 9}{7k - 6} = \frac{12}{5}\).
Cross-multiplying: 5(9k + 9) = 12(7k – 6), i.e. 45k + 45 = 84k – 72, so 39k = 117 and k = 3.
Initially Science had 9 × 3 = 27 students and Commerce had 7 × 3 = 21 students, so together there were 27 + 21 = 48 students.
Check: after the changes Science has 27 + 9 = 36 and Commerce has 21 – 6 = 15 students, and 36 : 15 = 12 : 5, as given.
Hence, 48.
The mean proportion of 5 and 20 is:
The fourth proportional to three numbers a, b and c is 84. The ratio of a to b is 5 : 6 and the ratio of b to c is 3 : 5. What is the value of a?
The mean proportional between 16 and 12.25 is:
Select the smallest ratio among following.
A- 5 : 7
B- 4 : 5
C- 9 : 10
D- 3 : 4
The length and breadth of a rectangular tank are such that when each is increased by 6 m, their ratio becomes 7 : 5. When each is decreased by 8 m, their ratio becomes 1 : 3. Find the breadth of the tank.
If x : 12 = 5 : 6, what is the value of x?
A has 72 articles whereas B has X same kind of articles. If the ratio of articles of A and B is 9 : 11. Then the value of 72 + X is:
The ratio of three numbers is 2 : 3 : 5 and their sum is 200. What is the value of the largest number?
A dump truck runs 54 km on 12 liters of fuel. How many kilometres will it run on 60 liters of fuel?
A sum of money is distributed among Amit, Bharat and Chetan in the ratio of 5 : 7 : 9. If the share of Bharat is ₹490 less than the combined share of Amit and Chetan, then what is the total sum of money distributed among them?
Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are under 25 years of age. Which one of the following statements is certainly correct ?
A bag contains Rs. 420 in the form of 5 rupee, 2 rupee, and 1 rupee coins. The number of coins of 5 rupee, 2 rupee, and 1 rupee is in the ratio of 2 : 3 : 5. What is the total number of coins in the bag?
If P/Q = 8/9 and Q - P = 12, then what is the value of P?
A child gets 1 random coin out of Re 1, Rs 2, and Rs 5 coins daily. He starts on 1st April and at the end of the month, he has coins in the ratio 5 ∶ 4 ∶ 6. Find the value of the coins with him
Find the proportion equivalent to M : N : O : P if M : N = 8 : 15, N : O = 5 : 9 and O : P = 18 : 19 ?