Q. 1
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Divide 560 into three parts proportional to 7, 4, 3.
💡
Step-by-Step Explanation & Concept Rationale
Sum of ratio is 14. Parts: 560/14×(7,4,3)=40×(7,4,3)=280,160,120.
Q. 2
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Divide 702 into three parts proportional to 1/2, 1/3 and 1/4.
💡
Step-by-Step Explanation & Concept Rationale
LCM(2,3,4)=12. Ratio: 6:4:3 (Sum 13). 702/13=54.54×(6,4,3)=324,216,162.
Q. 3
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Divide Rs. 80 in the proportion of 3 : 6 : 7.
💡
Step-by-Step Explanation & Concept Rationale
Sum 16. 80/16=5. Parts: 5×(3,6,7)=15,30,35.
Q. 4
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
81 into 3 parts: half of 1st, 1/3 of 2nd, 1/4 of 3rd are equal.
💡
Step-by-Step Explanation & Concept Rationale
Parts x,y,z where x/2=y/3=z/4. Ratio 2:3:4 (Sum 9). 81/9=9. 9×(2,3,4)=18,27,36.
Q. 5
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Rs. 225 into two parts in ratio 2 : 7.
💡
Step-by-Step Explanation & Concept Rationale
Sum 9. 225/9=25. Parts: 25×(2,7)=50,175.
Q. 6
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If 3 : 4 = 6 : X, then the value of X is:
💡
Step-by-Step Explanation & Concept Rationale
3/4=6/X⟹3X=24⟹X=8.
Q. 7
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If 9 : X = X : 16, then X is:
💡
Step-by-Step Explanation & Concept Rationale
X2=9×16=144⟹X=12.
Q. 8
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Which ratio is greater: 3/4 or 5/6?
💡
Step-by-Step Explanation & Concept Rationale
3/4 = 0.75; 5/6 ≈ 0.833. 5/6 is greater.
Q. 9
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
What is the third proportional to 16 and 36?
💡
Step-by-Step Explanation & Concept Rationale
16/36=36/x⟹x=(36×36)/16=1296/16=81.
Q. 10
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
What is the mean proportional between 5 and 80?
💡
Step-by-Step Explanation & Concept Rationale
Mean=5×80=400=20.
Q. 11
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
What is the value of X in 10 : 35 :: X : 42?
💡
Step-by-Step Explanation & Concept Rationale
10/35=X/42⟹2/7=X/42⟹X=(42×2)/7=12.
Q. 12
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If A : B = 3 : 4 and B : C = 8 : 9, then A : B : C is?
💡
Step-by-Step Explanation & Concept Rationale
Normalize B: A:B=6:8. B:C=8:9. Result: 6:8:9.
Q. 13
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If 14 : 35 : 21 : X, then value of X is?
💡
Step-by-Step Explanation & Concept Rationale
14/35=21/X
⟹X=(35×21)/14
⟹X=(35×21)/14
Q. 14
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
The third proportional of 36 and 16 is:
💡
Step-by-Step Explanation & Concept Rationale
36/16=16/x
⟹x=(16×16)/36.
⟹x=(16×16)/36.
Q. 15
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
The mean proportional of 0.32 and 0.02 is:
💡
Step-by-Step Explanation & Concept Rationale
$\sqrt{0.32×0.02}=\sqrt{0.0064}=0.08$.
Q. 16
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Which of the following is the greatest: 7:9, 2:4, 3:1, 7:1?
💡
Step-by-Step Explanation & Concept Rationale
Values: 0.77,0.5,3.0,7.0. 7:1 is the greatest.
Q. 17
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If a:b=3:4, b:c=4:5 and c:d=5:6, then a:d = ?
💡
Step-by-Step Explanation & Concept Rationale
a/d=(a/b)×(b/c)×(c/d)=3/4×4/5×5/6=3/6=1/2.
Q. 18
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Value of x in the ratio 40 : 30 :: 10 : x is?
💡
Step-by-Step Explanation & Concept Rationale
40/30=10/x
⟹4/3=10/x
⟹x=30/4=15/2.
⟹4/3=10/x
⟹x=30/4=15/2.
Q. 19
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
In what proportion must a man mix beer at Rs. 11 a litre with beer at Rs. 6 a litre, s0 that the mixture may be worth Rs. 8 a litre?
💡
Step-by-Step Explanation & Concept Rationale
Alligation: (8−6):(11−8)=2:3.
Q. 20
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If x : y = y : z, then x = ?
💡
Step-by-Step Explanation & Concept Rationale
$x/y=y/z
⟹xz=y^2
⟹x=y^2/z$.
⟹xz=y^2
⟹x=y^2/z$.
Q. 21
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
The inverse ratio of 12 to 18 is:
💡
Step-by-Step Explanation & Concept Rationale
Inverse ratio of 12 : 18 is 18 : 12 = 3 : 2.
Q. 22
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Numbers in ratio 2:3; add 8 to each, ratio becomes 3:4.
💡
Step-by-Step Explanation & Concept Rationale
2x+8/3x+8=3/4⟹8x+32=9x+24⟹x=8. Numbers: 16, 24.
Q. 23
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
The wages of two persons are in the ratio of 4:7. Both of them spend of 4:7. Both of them spend 80% of wages and save rest of the money. The ratio of their savings is
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Step-by-Step Explanation & Concept Rationale
Since both individuals save the exact same percentage of their money, the ratio of their savings will always be identical to the ratio of their wages.
Q. 24
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Sides of two squares are in the ratio of 3:4. Their perimeters are in the ratio of
💡
Step-by-Step Explanation & Concept Rationale
Perimeter of a square (4s) maintains the same ratio as the sides (s).
Q. 25
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Rs. 49 divided among 150 children: each girl has 8 as, each boy has 4 as. How many boys are there?
💡
Step-by-Step Explanation & Concept Rationale
Convert the units:
In old currency terms, 1 Rupee (Rs.) equals 16 annas (as).
Total money = \(49 \times 16 = \mathbf{784 \text{ annas}}\).
(Alternatively, this classic problem is often phrased as 50 paise and 25 paise, which yields the exact same ratio and mathematical result).
Set up the equations:
Let the number of boys be \(b\) and girls be \(g\).
Total children: \(b + g = 150 \implies g = 150 - b\)
Total share: \(4b + 8g = 784\)
Substitute \(g\) into the share equation:
\(4b+8(150-b)=784\)
\(4b+1200-8b=784\)
\(1200-4b=784\)
\(4b=1200-784\)
\(4b=416\)\(b=\frac{416}{4}=\mathbf{104}\)
There are 104 boys in the group.
In old currency terms, 1 Rupee (Rs.) equals 16 annas (as).
Total money = \(49 \times 16 = \mathbf{784 \text{ annas}}\).
(Alternatively, this classic problem is often phrased as 50 paise and 25 paise, which yields the exact same ratio and mathematical result).
Set up the equations:
Let the number of boys be \(b\) and girls be \(g\).
Total children: \(b + g = 150 \implies g = 150 - b\)
Total share: \(4b + 8g = 784\)
Substitute \(g\) into the share equation:
\(4b+8(150-b)=784\)
\(4b+1200-8b=784\)
\(1200-4b=784\)
\(4b=1200-784\)
\(4b=416\)\(b=\frac{416}{4}=\mathbf{104}\)
There are 104 boys in the group.
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