Aptitude - Ratio and Proportion
16.
What number has to be added to each term of 3 : 5 to make the ratio 5 : 6 ?
Answer
Let the numbers to be added be x. Then,
3 + x5 + x = 56 ⇒ 6(3 + x) = 5(5 + x) ⇒ x = (25 − 18) = 7
Hence, the number to be added is 7.
Answer :
Option BExplanation :
Let the numbers to be added be x. Then,
3 + x5 + x = 56 ⇒ 6(3 + x) = 5(5 + x) ⇒ x = (25 − 18) = 7
Hence, the number to be added is 7.
17.
The ratio of the number of students studying in schools A, B and C is 5 : 6 : 8. If the number of students in each of the schools is increased by 30%, 25% and 25% respectively, what will be the new ratio of the students in schools A, B and C ?
Answer
Let the numbers of students in A, B, C be 5x, 6x and 8x respectively.
New strength = (130% of 5x), (125% of 6x) and (125% of 8x)
=
130100 x 5x 
, 125100 x 6x , 125100 x 8x
New ratio = 650x100 : 750x100 : 1000x100 : = 65 : 75 : 100 = 13 : 15 : 20
Answer :
Option BExplanation :
Let the numbers of students in A, B, C be 5x, 6x and 8x respectively.
New strength = (130% of 5x), (125% of 6x) and (125% of 8x)
=
130100 x 5x , 125100 x 6x , 125100 x 8x New ratio = 650x100 : 750x100 : 1000x100 : = 65 : 75 : 100 = 13 : 15 : 20
18.
If 0.75 : x :: 5 : 8, then x = ?
Answer
x x 5 = 0.75 x 8 = 6
⇒ x = 65 = 1.2
Answer :
Option BExplanation :
x x 5 = 0.75 x 8 = 6
⇒ x = 65 = 1.2
19.
When 1 is added to each of the given two numbers, their ratio becomes 3 : 4 and when 5 is subtracted from each, the ratio becomes 7 : 10. The numbers are :
Answer
Let the two numbers be x and y. Then,
x + 1y + 1 = 34 ⇒ 4x + 4 = 3y + 3 ⇒ 3y − 4x = 1 ... (i)
x − 5y − 5 = 710 ⇒ 10x − 50 = 7y − 35 ⇒ 7y − 10x = −15 ... (ii)
On solving, (i) and (ii) we get x = 26 and y = 35
Answer :
Option CExplanation :
Let the two numbers be x and y. Then,
x + 1y + 1 = 34 ⇒ 4x + 4 = 3y + 3 ⇒ 3y − 4x = 1 ... (i)
x − 5y − 5 = 710 ⇒ 10x − 50 = 7y − 35 ⇒ 7y − 10x = −15 ... (ii)
On solving, (i) and (ii) we get x = 26 and y = 35
20.
In an alloy, the ratio of copper and zinc is 5 : 2. If 1.25 kg of zinc is mixed in 17.5 kg of alloy, then the ratio of copper and zinc in the alloy will be
Answer
Copper in 17.5 kg of alloy = 17.5 x 57 kg = 12.5 kg
Zinc in it = (17.5 − 12.5)kg = 5 kg
On addition of zinc, total zinc = (5 + 1.25)kg = 6.25 kg
Ratio of copper and zinc in the new alloy = 12.56.25 = 21 = 2 : 1
Answer :
Option BExplanation :
Copper in 17.5 kg of alloy =
17.5 x 57 kg = 12.5 kgZinc in it = (17.5 − 12.5)kg = 5 kg
On addition of zinc, total zinc = (5 + 1.25)kg = 6.25 kg
Ratio of copper and zinc in the new alloy = 12.56.25 = 21 = 2 : 1
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