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⁞ Ratio And Proportion

Aptitude ➤ Ratio And Proportion ➤ 1
Question 6
Q6.  Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
 

Answer :  2 : 3 : 4


Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.

Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).

⇒ (140 × 5x)/100 , (150 × 7x)/100 and (175 × 8x)/100
⇒ 7x, (21x/2) and 14x.

∴ The required ratio = 7x : (21x/2) : 14x
⇒ 14x : 21x : 28x
⇒ 2 : 3 : 4.
⚔ DISCUSS

Question 7
Q7.  The sum of two numbers is 80 and their difference is 8. What is the ratio of the two numbers ?
 

Answer :  11 : 9


The required ratio of the numbers = (80+8)/(80-8) = 88/72 = 11/9 or 11 : 9

♥ If the sum of two numbers is x and their difference is y then the ratio of numbers is given by (x+y) : (x-y)
⚔ DISCUSS

Question 8
Q8.  Find the mean proportional between 3 and 75.
 

Answer :  15


Let x be the required mean proportional . Then,
3 : x :: x : 75

∴ x = √(3×75) = 15.

♥ If three quantities a, b and c are in continued proportion, then a : b = b : c
∴ ac = b2
⚔ DISCUSS

Question 9
Q9.  The fourth proportional to 5, 8, 15 is
 

Answer :  24


Let the fourth proportional to 5, 8, 15 be x.
Then, 5 : 8 :: 15 : x
⇒ 5x = (8 x 15)
⇒ x = (8 x 15)/5 = 120/5 = 24.
⚔ DISCUSS

Question 10
Q10.  In a bag, there are coins of 25p, 10p and 5p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5p coins are there ?
 

Answer :  150


Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.

Then, sum of their values = Rs. [(25x)/100] + [(10 × 2x)/100] + [(5 × 3x)/100]
= Rs. 60x/100

∴ 60x/100 = 30
⇒ x = (30 x 100)/60 = 50.

Hence, the number of 5 p coins = (3 x 50) = 150.
⚔ DISCUSS

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