Ratio and Proportion is one of the most important and scoring topics in the SSC GD Mathematics section. Questions from this topic are frequently asked and are usually based on direct formulas, logical understanding, and basic calculations. Practising Ratio and Proportion questions with proper solutions can significantly improve accuracy and confidence in the SSC GD exam.
SSC GD Ratio and Proportion Questions with Solutions
Q.1 The ratio of number of boys and girls in a school of 3528 students is 5:4. How many more girls should be admitted in the school to make this ratio 1:1?
A. 312
B. 392
C. 472
D. 552
Answer: B
Solution:
Total students = 3528
Ratio = 5 : 4 → Total parts = 9
One part = 3528 ÷ 9 = 392
Boys = 5 × 392 = 1960
Girls = 4 × 392 = 1568
Required girls = 1960 − 1568 = 392
Q.2 If (x + z)/y = z/(x − y) = x/z, then x : y : z is equal to?
A. 4 : 3 : 6
B. 3 : 4 : 2
C. 4 : 3 : 2
D. 3 : 4 : 6
Answer: D
Solution: As per given proportional equations, solving gives the ratio 3 : 4 : 6.
Q.3 When k is added to each of 11, 27, 20 and 44, then the numbers so obtained are in proportion. What is the mean proportional between (k+2) and (3k−5)?
A. 6
B. 15
C. 9
D. 12
Answer: D
Solution:
(11+k)(44+k) = (27+k)(20+k)
k = 7
Mean proportional = √(9 × 16) = 12
Q.4 The students in sections A, B and C are in the ratio 5:4:7. After admission of new students, the ratio becomes 10:9:11. Find total students.
A. 210
B. 120
C. 150
D. 90
Answer: B
Solution: Solving the ratio gives total students = 120.
Q.5 If 38% of first number is equal to two-sevenths of second number, what is the ratio?
A. 101 : 129
B. 103 : 132
C. 100 : 133
D. 96 : 131
Answer: C
Q.6 If 25% of A = 20% of B = 10% of C, find A : B : C.
A. 4 : 5 : 10
B. 10 : 5 : 4
C. 5 : 4 : 10
D. 2 : 3 : 5
Answer: A
Q.7 When x is subtracted from 55, 50, 23 and 22, they are in proportion. What is the fourth proportion of 3, 7 and x?
A. 35
B. 32
C. 38
D. 36
Answer: A
Q.8
A bag contains ₹10, ₹5 and ₹2 coins in the ratio 1:2:3. Total amount is ₹390. Find number of coins.
A. 10, 20, 30
B. 15, 30, 45
C. 20, 40, 60
D. 12, 24, 36
Answer: B
Q.9 The mean proportional between 36 and N is three times the mean proportional between 8 and 32. Find N.
A. 47
B. 58
C. 51
D. 64
Answer: D
Q.10 x varies inversely as the square of y. If y = 5 when x = 6, find x when y = 4.
A. 9.175
B. 9.835
C. 9.375
D. 9.925
Answer: C
Q.11 When x is subtracted from each of 43, 38, 11 and 6, the numbers so obtained are in proportion. Find the value of x.
Solution:
(43 − x) / (38 − x) = (11 − x) / (6 − x)
(43 − x)(6 − x) = (38 − x)(11 − x)
258 − 49x + x² = 418 − 49x + x²
x = 4
Q.12 If 2x = 3y = 4z, then x : y : z is equal to?
Solution:
Let 2x = 3y = 4z = k
x = k/2, y = k/3, z = k/4
x : y : z = (k/2) : (k/3) : (k/4)
= 6 : 4 : 3
Q.13 Divide ₹3777 among A, B and C in such a way that A : B : C = 7 : 9 : 3.
Solution:
Sum of ratios = 7 + 9 + 3 = 19
A = (7/19) × 3777 = ₹1391
B = (9/19) × 3777 = ₹1789
C = (3/19) × 3777 = ₹597
Q.14 If x : y = 4 : 5 and y : z = 10 : 7, find x : y : z.
Solution:
x : y = 4 : 5 = 8 : 10
y : z = 10 : 7
x : y : z = 8 : 10 : 7
Q.15 The ratio of the ages of A and B is 3 : 5. After 6 years, the ratio becomes 5 : 7. Find the present age of A.
Solution:
Let ages be 3x and 5x
(3x + 6)/(5x + 6) = 5/7
21x + 42 = 25x + 30
x = 3
Age of A = 3 × 3 = 9 years
Q.16 The ratio of boys to girls in a class is 7 : 9. If there are 63 boys, find the number of girls.
Solution:
7 parts = 63
1 part = 9
Girls = 9 × 9 = 81
Q.17 If a : b = 5 : 6 and b : c = 7 : 8, find a : b : c.
Solution:
a : b = 35 : 42
b : c = 42 : 48
a : b : c = 35 : 42 : 48
Q.18 The sum of three numbers is 98. Their ratio is 2 : 3 : 7. Find the largest number.
Solution:
Sum of ratios = 12
One part = 98 ÷ 12 = 8.1667
Largest number = 7 × 8.1667 = 57.17
Q.19 If x : y = 3 : 4 and y : z = 8 : 9, find x : y : z.
Solution:
x : y = 6 : 8
y : z = 8 : 9
x : y : z = 6 : 8 : 9
Q.20 Divide ₹14000 among A, B and C in the ratio 7 : 9 : 3.
Solution:
Total parts = 19
A = (7/19) × 14000 = ₹5158
B = (9/19) × 14000 = ₹6632
C = (3/19) × 14000 = ₹2210
Q.21 If 3.6 : 1.2 :: 1.2 : y, then the value of y is:
A. 0.60
B. 0.40
C. 0.90
D. 0.80
Answer: B
Solution:
3.6 : 1.2 :: 1.2 : y
(1.2 × 1.2) = (3.6 × y)
1.44 = 3.6y
y = 0.4
Q.22 What number should be added to each of 8, 35, 7 and 31 so that the resulting numbers will be in proportion?
A. 2
B. 3
C. 5
D. 1
Answer: D
Solution:
(8 + x):(35 + x) = (7 + x):(31 + x)
(8 + x)(31 + x) = (35 + x)(7 + x)
248 + 39x = 245 + 42x
x = 1
Q.23 If 77% of first number is equal to three-fourths of second number, what is the ratio of first number to the second number?
A. 75 : 77
B. 74 : 75
C. 73 : 82
D. 72 : 73
Answer: A
Solution:
77% of x = 3/4 of y
(77/100)x = (3/4)y
x : y = 75 : 77
Q.24 The ratio of incomes of Seema and Darshan is 7 : 8. They save ₹15,000 and ₹9,000 respectively. If the ratio of their expenditures is 11 : 16, then what is the total expenditure?
A. 68,000
B. 64,000
C. 64,125
D. 63,000
Answer: C
Solution:
8(15000 + 11x) = 7(9000 + 16x)
x = 2375
Total Expenditure = 26125 + 38000 = 64125
Q.25 Some marbles are packed in boxes A, B, C and D in the ratio 6 : 3 : 7 : 5. If box B has 400 less marbles than box D, find total marbles.
A. 4000
B. 4100
C. 4200
D. 3900
Answer: C
Solution:
5x − 3x = 400 → x = 200
Total = (6+3+7+5) × 200 = 4200
Q.26 X is directly proportional to A² and A is inversely proportional to Y. If X = 39 when Y = 20, find X when Y = 2.
A. 3902
B. 3901
C. 3897
D. 3900
Answer: D
Solution:
X ∝ 1/Y²
X₁/X₂ = (Y₂/Y₁)²
X = 39 × (20/2)² = 3900
Q.27 C is the third proportional of 29 and B. If B is the sum of first three even natural numbers, find C.
A. 3.53
B. 3.85
C. 7.64
D. 4.97
Answer: D
Solution:
B = 2 + 4 + 6 = 12
C = (12²)/29 = 4.97
Q.28 y varies directly as (x + 3). If y = 8 when x = 1, find y when x = 2.
A. 10
B. 5
C. 8
D. 2
Answer: A
Solution:
y = k(x + 3)
k = 2
y = 2(5) = 10
Q.29 Three numbers are in the ratio 65 : 224 : 260. If the difference between largest and smallest is 30, find the largest number.
A. 40
B. 39
C. 41
D. 42
Answer: A
Solution:
260x − 65x = 30
x = 2/13
Largest number = 260 × (2/13) = 40
Q.30 Four numbers are in the ratio 16 : 10 : 9 : 17. If their sum is 6292, find the sum of first and third number.
A. 3025
B. 3070
C. 3031
D. 3074
Answer: A
Solution:
52x = 6292 → x = 121
(16 + 9)x = 25 × 121 = 3025
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