CRE 1 - Ratio | Arithmetic - Ratio, Proportion & Variation
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Anand divided 70 sweets among his daughters Rohini and Sushma in the ratio 4 : 3. How many sweets did Rohini get?
Answer: 40
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Explanation :
Since, the ratio of sweets that Rohini and Sushma get is 4 : 3, let the number of sweets received by Rohini is 4x and Sushma is 3x.
According to question, 4x + 3x = 70
⇒ 7x = 70
⇒ x = 10
∴ Sweets received by Rohini = 4x = 4 × 10 = 40.
Alternately,
Number of sweets that Rohini got = × 70 = 40
Hence, 40.
Workspace:
If x : y = 4 : 3, find 5x : 7y.
- (a)
15/28
- (b)
3/4
- (c)
20/21
- (d)
20/37
Answer: Option C
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Explanation :
Hence, option (c).
Workspace:
Ratio of two numbers is 4 : 5 and their sum is 144. Find the smaller of the two numbers.
Answer: 64
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Explanation :
Let the numbers be 4x and 5x.
4x + 5x = 144
x = 16
Smaller of the two numbers = 4x = 64.
Alternately,
Smaller number = 4/9 × 144 = 64.
Hence, 64.
Workspace:
The greatest ratio out of 2 : 3, 5 : 4, 3 : 2 and 4 : 5 is?
- (a)
4 : 5
- (b)
3 : 2
- (c)
5 : 4
- (d)
2 : 3
Answer: Option B
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Explanation :
Here, only 5/4 and 3/2 are greater than 1. So, let’s consider only these two ratios. Other 2 ratios are smaller than 1.
To find the greatest ratio, we must bring each of the ratio to common denominator.
Thus, ≡ ≡
Hence, ratio 3 : 2 is the greatest ratio.
Hence, option (b).
Alternately,
If a/b > 1, ⇒
Hence, = < .
Alternately,
Assume
⇒ 5 × 2 > 3 × 4
⇒ 10 > 12, which is not true.
Hence our assumption was wrong.
∴ 3/2 is the greatest ratio.
Hence, option (b).
Workspace:
The smallest ratio out of 1 : 2, 2 : 1, 1 : 3 and 3 : 1 is?
- (a)
3 : 1
- (b)
1 : 3
- (c)
2 : 1
- (d)
1 : 2
Answer: Option B
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Explanation :
Here, only 1/2 and 1/3 are less than 1. So, let’s consider only these two ratios. Other 2 ratios are greater than 1.
We have to find the smallest ratio here 1/2,1/3
Since numerator is same, the ratio with greater denominator will be smallest.
∴ 1/3 is the smallest of the ratios given.
Hence, option (b).
Workspace:
The ratio of two numbers is 3 : 5 and their sum is 72. Find the larger of the two numbers.
Answer: 45
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Explanation :
Let the numbers be 3k and 5k, where k is a constant.
Sum of 3k and 5k is 8k.
Now 8k = 72
⇒ k = 9
∴ The greater number is 5 × 6 i.e., 45.
Hence, 45.
Alternately,
Larger of the two numbers = 5/8 × 72 = 45.
Hence, 45.
Workspace:
The present ages of two persons are in the ratio 15 : 17. Twenty-four years ago the ratio of their ages was 9 : 11. Find the present age of the older person.
- (a)
64 years
- (b)
72 years
- (c)
56 years
- (d)
68 years
Answer: Option D
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Explanation :
Let their present ages be 15x and 17x years respectively.
Ratio of their ages 24 years ago:
⇒ 165x – 264 = 153x - 216
⇒ 12x = 48
⇒ x = 4
∴ The age of the older person is 17 × 4 i.e., 68 years
Hence, option (d).
Workspace:
The ratio of the number of students in 3 sections A, B and C is 3 : 7 : 8. If there are a total of 360 students in these sections, find the number of students in section A.
Answer: 60
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Explanation :
Let the number of students in A, B and C be 3x, 7x and 8x respectively.
3x + 7x + 8x = 360
⇒ x = 20
⇒ 3x = 60
Hence, 60.
Alternately,
Number of students in section A = × 360 = 60
Hence, 60.
Workspace:
156 is divided into two parts such that seven times the first part and five times the second part are in the ratio 5 : 2. Find the first part.
Answer: 100
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Explanation :
Let the numbers be x and 156 – x
⇒ 14x = 25 × 156 - 25x
⇒ 39x = 25 × 156
⇒ x = 25 × 4 = 100
∴ The first part is 100.
Hence, 100.
Alternately,
Let the numbers be a and b.
Hence, a + b = 156, and
⇒
⇒ a = 25/39 × 156 = 100.
Hence, 100.
Workspace:
The present ages of Anand and Ashish are in the ratio 4 : 5. 10 years hence, the ratio of their ages will be 5 : 6. Find the present age of Anand. (in years)
Answer: 40
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Explanation :
Let the present ages of Anand and Ashish be 4x years and 5x years respectively.
The ratio of their ages 10 years hence =
⇒ 24x + 60 = 25x + 50
⇒ 10 = x
Therefore, Anand’s present age is 4 × 10 = 40 years.
Hence, 40.
Workspace:
If a : b = 3 : 7, find the value of (4a + b) : (3a + 5b).
- (a)
12 : 41
- (b)
19 : 32
- (c)
12 : 47
- (d)
19 : 44
Answer: Option D
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Explanation :
Let a = 3k, b = 7k
∴ =
Hence, option (d).
Alternately,
We have to find the value of
Dividing both numerator and denominator with b, we get
=
Hence, option (d).
Workspace:
Find the numbers which are in the ratio 3 : 2 : 4 such that the sum of the first and the second numbers added to the difference of the third and the second numbers is 42.
- (a)
24, 16, 32
- (b)
12, 8, 16
- (c)
18, 12, 48
- (d)
18, 12, 24
Answer: Option D
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Explanation :
Let the numbers be p, q and r.
Given that p, q and r are in the ratio 3 : 2 : 4.
p : q : r = 3 : 2 : 4
Let p = 3x, q = 2x and r = 4x
Given (p + q) + (r – q) = 42
⇒ p + q + r – q = 42 ⇒ p + r = 42
⇒ 3x + 4x = 42
⇒ 7x = 42
⇒ x = 6
p, q, r are 3x, 2x, 4x.
∴ p, q, r are 18, 12, 24
Hence, option (d).
Workspace:
In a group of 60 students, which of the following can’t be the ratio of males and females?
- (a)
2 : 3
- (b)
1 : 5
- (c)
2 : 7
- (d)
2 : 1
Answer: Option C
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Explanation :
Let the ratio of males and females be m : f.
We know the number of males will be
Consider option (c), m = 2 and f = 7. This cannot be the ratio because 60 is not divisible by (2 + 7) i.e. 9.
Hence, option (c).
Workspace:
If a : b = 3 : 2 and b : c = 7 : 5, then find a : b : c.
- (a)
10 : 15 : 21
- (b)
21 : 14 : 10
- (c)
9 : 12 : 14
- (d)
12 : 7 : 18
Answer: Option B
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Explanation :
a/b = 3/2 = 21/14 (Multiplying and dividing by 7 to make the value of b same in both ratios)
b/c = 7/5 = 14/10 (Multiplying and dividing by 2 to make the value of b same in both ratios)
a : b : c = 21 : 14 : 10
Hence, option (b).
Workspace:
If A is 1/3rd of B and B is 1/2 of C, then A : B : C is?
- (a)
1 : 3 :6
- (b)
2 : 3 : 6
- (c)
3 : 2 : 6
- (d)
None of these
Answer: Option A
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Explanation :
A = B/3, B = C/2, C = C, then,
A : B : C = = = = 1 : 3 : 6
Hence, option (a).
Workspace:
If A : B = 3 : 2, B : C = 4 : 3, C : D = 5 : 4, then A : D is?
- (a)
5 : 2
- (b)
30 : 20
- (c)
15 : 12
- (d)
None of these
Answer: Option A
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Explanation :
A/B = 3/2, B/C = 4/3, C/D = 5/4
Here, B = 2A/3 and B = 4C/3
⇒ 2A/3 = 4C/3 ⇒ C = A/2
∴ C/D = A/2D = 5/4
⇒ A/D = (5 × 2)/4 = 5/2 or 5 : 2
Hence, option (a).
Alternately,
A : B : C : D = 3 × 4 × 5 : 2 × 4 × 5 : 2 × 3 × 5 : 2 × 3 × 4
∴ A : B : C : D = 60 : 40 : 30 : 24
∴ A : D = 60 : 24 = 5 : 2
Hence, option (a).
Workspace:
The ratio of two numbers is 3 : 2 and their difference is 225, the smaller number is:
- (a)
90
- (b)
675
- (c)
135
- (d)
450
Answer: Option D
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Explanation :
Let the two numbers be x and y whose ratio is 3 : 2, That is
x/y = 3/2 and x – y = 225
Let x = 3a and y = 2a.
∴ 3a – 2a = 225 ⇒ a = 225
⇒ x = 3 × 225 = 675 and y = 2 × a = 450.
Hence, smaller number of the ratio is 450.
Hence, option (d).
Workspace:
If , then find .
- (a)
4/5
- (b)
5/4
- (c)
6/7
- (d)
3/4
Answer: Option B
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Explanation :
Given that,
⇒ 4(p + q) = 3(2p + q)
⇒ 4p + 4q = 6p + 3q ⇒ q = 2p
Now,
Hence, option (b).
Workspace:
If p + q + r = 180 and p = q/2 and q = r/3, find r.
Answer: 120
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Explanation :
p = ⇒
q = ⇒
So, p : q : r = 1 : 2 : 6
So, r = × 180 = 120.
Hence, 120.
Workspace:
If p : q = 3 : 1, find .
- (a)
2/7
- (b)
1/8
- (c)
3/7
- (d)
Cannot be determined
Answer: Option D
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Explanation :
Given that p : q = 3 : 1
p/q = 3/1
p = 3q
(∵ p = 3q)
=
Since we don’t know the value of ‘q’, the answer cannot be determined.
Hence, option (d).
Workspace:
What should be subtracted from the numbers in the ratio 9 : 16 so as to get 1 : 2?
- (a)
8
- (b)
14
- (c)
2
- (d)
Cannot be determined
Answer: Option D
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Explanation :
Two numbers are in the ratio of 9 : 16. Let the numbers be 9x and 16x.
Now, let a be subtracted to get new ratio as 1 : 2.
∴
⇒ 18x - 2a = 16x - a
⇒ 2x = a
Since we do not know the value of x, we cannot find out the value of a.
Hence, option (d).
Workspace:
If A : B = 2 : 3, B : C = 3 : 4 and C : D = 4 : 5, then, A : B : C : D is?
- (a)
2 : 3 : 4 : 5
- (b)
5 : 2 : 3 : 7
- (c)
3 : 4 : 7 : 8
- (d)
None of these
Answer: Option A
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Explanation :
A/B = 2/3, B/C = 3/4, C/D = 4/5
⇒ If A = 2, B = 3, C = 4 and D = 5
∴ A : B : C : D = 2 : 3 : 4 : 5
Hence, option (a).
Workspace:
At a party, there are a total of 56 people. If ‘m’ men join the party, the ratio of the number of ladies to that of men will change from 4 : 3 to 4 : 5. Find m.
Answer: 16
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Explanation :
Number of ladies at the party do not change.
Initial number of ladies = (4/7) × 56 = 32.
Initial number of men = 56 - 32 - 24.
After x men join,
the number of men would be 5/4 × (Number of ladies) = 5/4 × 32 = 40
∴ the number of men joining (m) = 40 – 24 = 16.
Hence, 16.
Workspace:
Rs. 1500 is divided among, A, B and C such that A receives 1/3rd as much as B and C together. A’s share is?
- (a)
Rs. 600
- (b)
Rs. 525
- (c)
Rs. 375
- (d)
Rs. 0
Answer: Option C
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Explanation :
Money received by A, B and C be a, b, c respectively then
a + b + c = 1500 …(i)
also, a = (b + c)/3 ⇒ b + c = 3a …(ii)
Then from (i) and (ii)
a + 3a = 1500
⇒ 4a = 1500 ⇒ a = 375
∴ A’s share is Rs. 375.
Hence, option (c).
Workspace:
The monthly salaries of A and B are in the ratio 2 : 3. The monthly expenditures of X and Y are in the ratio 3 : 4. Find the ratio of the monthly savings of X and Y.
- (a)
5 : 3
- (b)
3 : 5
- (c)
4 : 7
- (d)
Cannot be determined
Answer: Option D
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Explanation :
Let the monthly salaries of A and B be Rs. 2x and Rs. 3x respectively.
Let the monthly expenditures of A and B be Rs. 3y and Rs. 4y respectively.
Ratio of the monthly savings of A and B = .
As x/y is unknown, the ratio cannot be found
Hence, option (d).
Workspace:
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