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Ratio - Aptitude MCQ Questions and Solutions with Explanations

Ratio MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on Ratio with easy and logical explanations. Ratio MCQ is important for exams like Banking exams,IBPS,SCC,CAT,XAT,MAT etc. Page-1 section-3

Each section contains 100 MCQs on Ratio .
1
The sum of three numbers is 116. The second number and the third number are in the ratio of 9 : 16 while the first number and the third number are in the ratio of 1 : 4. Find the second number.
Discuss
Answer & Solution
Answer: Option E
Solution:
$$\eqalign{ & {\text{Second}}:{\text{Third}} \cr & = {\text{9}}:{\text{16}} \cr & {\text{Third}}:{\text{first}} \cr & = {\text{4}}:{\text{1}} \cr & {\text{ = 16}}:{\text{4}}{\text{}} \cr & \therefore {\text{Second}}:{\text{Third}}:{\text{first}} \cr & = {\text{9}}:{\text{16}}:{\text{4}}{\text{}} \cr & {\text{Second number}} \cr & = \left( {{\text{116}} \times \frac{{\text{9}}}{{{\text{29}}}}} \right) \cr & = {\text{36}} \cr} $$
2
Rs. 2010 are to be divided among A, B, C in such a way that if A gets Rs. 5, then B must get Rs. 12 and if B gets Rs. 4, then C must get Rs. 5.50. The share of C will exceed that of B by -
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & {\text{A}}:{\text{B}} = 5:12 \cr & {\text{B}}:{\text{C}} = 4:5.50 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 12:16.5 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 12:\frac{{33}}{2} \cr & {\text{A}}:{\text{B}}:{\text{C}} = 5:12:\frac{{33}}{2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10:24:33 \cr & {\text{Sum of ratio terms}} \cr & = 10 + 24 + 33 \cr & = 67 \cr & {\text{C's share}} = {\text{Rs}}{\text{.}}\left( {2010 \times \frac{{33}}{{67}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}990 \cr & B'{\text{s share}} = {\text{Rs}}{\text{.}}\left( {2010 \times \frac{{24}}{{67}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.720 \cr & {\text{Required difference}} \cr & = {\text{Rs}}{\text{.}}\left( {990 - 720} \right) \cr & = {\text{Rs}}{\text{. }}270 \cr} $$
3
A person bought some rice and wheat for Rs. 380. The ratio of weight of rice and wheat is 4 : 3 and the price equal amount of rice and wheat is in the ratio 5 : 6. The rice was bought of worth = ?
Discuss
Answer & Solution
Answer: Option C
Solution:
  Rice   :   Wheat    
Weight 4 : 3    
Price 5 : 6    
Total Price   20 + 18  =  38
∴ 20 + 18 = 38 units
1 unit = Rs. 10
∴ Price of total rice
⇒ 20 × 10 = Rs. 200
4
The ratio of monthly income of A and B is 6 : 5 and their expenditure are in the ratio of 4 : 3. If each of them saves Rs. 400 per month, find the sum of their monthly incomes ?
Discuss
Answer & Solution
Answer: Option C
Solution:
Income of A : B = 6 : 5 = 6A : 4B
Expenditure of A : B = 4 : 3 = 4A : 3B
Saving of A and B = 400;
∴ 6A - 4A = 400
⇒ A = 200
And 5B - 3B = 400
⇒ B = 200
Income of A = 6 × 200 = 1200
Income of B = 5 × 200 = 1000
Sum of the Income of A and B = 1200 + 1000 = Rs. 2200
5
A box contains 420 coins of 1 rupee, 50 paise and 20 paise coins. The ratio of their values is 13 : 11 : 7. The number of 50 paise coins is = ?
Discuss
Answer & Solution
Answer: Option D
Solution:
  Rs. 1   :   50 P   :   20 P
Values 13x : 11x : 7x
Number of coins   13x×1 : 11x×2 : 7x×5
  13x : 22x : 35x
Given total coins
⇒ 13x + 22x + 35x = 420
⇒ 70x = 420
⇒ x = 6
∴ Numbers of 50 paise coins are
= 22x = 22 × 6 = 132
6
Rs. 600 are divided among A, B, C so that Rs. 40 more than $$\frac{{\text{2}}}{{\text{5}}}$$ of A's share, Rs. 20 more than $$\frac{{\text{2}}}{{\text{7}}}$$ of B's share and Rs. 10 more than $$\frac{{\text{9}}}{{{\text{17}}}}$$ of C's share may all be equal. What is A's share ?
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & = \frac{2}{5}{\text{A}} + 40 = \frac{2}{7}{\text{B}} + 20 \cr & \Rightarrow \frac{2}{7}{\text{B}} = \frac{2}{5}{\text{A}} + 20 \cr & \Rightarrow {\text{B}} = \frac{7}{2}\left( {\frac{2}{5}{\text{A}} + 20} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{7}{5}{\text{A}} + 70} \right) \cr & {\text{And,}} \cr & = \frac{2}{5}{\text{A}} + 40 = \frac{9}{{17}}{\text{C}} + 10 \cr & \Rightarrow \frac{9}{{17}}{\text{C}} = \frac{2}{5}{\text{A}} + 30 \cr & \Rightarrow {\text{C}} = \frac{{17}}{9}\left( {\frac{2}{5}{\text{A}} + 30} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{34}}{{45}}{\text{A}} + \frac{{170}}{3} \cr & = {\text{A}} + {\text{B}} + {\text{C}} = 600 \cr & \Rightarrow {\text{A}} + \left( {\frac{7}{5}{\text{A}} + 70} \right) + \left( {\frac{{34}}{{45}}{\text{A}} + \frac{{170}}{3}} \right) = 600 \cr & \Rightarrow \frac{{142{\text{A}}}}{{45}} = 600 - \frac{{380}}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{1420}}{3} \cr & \Rightarrow {\text{A}} = \frac{{1420}}{3} \times \frac{{45}}{{142}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 150 \cr} $$
7
If Rs.1066 are divided among A, B, C and D such that A : B = 3 : 4, B : C = 5 : 6 and C : D = 7 : 5, Who will get the maximum ?
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & {\text{A}}:{\text{B}} = {\text{3}}:{\text{4}}, \cr & {\text{B}}:{\text{C}} = {\text{5}}:{\text{6}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {5 \times \frac{4}{5}} \right):\left( {6 \times \frac{4}{5}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 4:\frac{{24}}{5} \cr & {\text{C}}:{\text{D}} = {\text{7}}:{\text{5}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {7 \times \frac{{24}}{{35}}} \right):\left( {5 \times \frac{{24}}{{35}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{24}}{5}:\frac{{24}}{7} \cr & \therefore {\text{A}}:{\text{B}}:{\text{C}}:{\text{D}} \cr & = 3:4:\frac{{24}}{5}:\frac{{24}}{7} \cr & = 105:140:168:120 \cr} $$
Clearly, C will get the maximum
8
Divide Rs. 671 among A, B and C such that if their shares be increased by Rs. 3, Rs. 7 and Rs. 9 respectively the remainder shall be in the ratio 1 : 2 : 3.
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & {\text{Remainder}} \cr & = {\text{Rs}}{\text{.}}\left[ {671 + \left( {3 + 7 + 9} \right)} \right] \cr & = {\text{Rs}}{\text{. }}690 \cr & {\text{A's share}} \cr & = {\text{Rs}}{\text{.}}\left[ {\left( {690 \times \frac{1}{6}} \right) - 3} \right] \cr & = {\text{Rs}}{\text{. }}112 \cr & {\text{B's share}} \cr & = {\text{Rs}}{\text{.}}\left[ {\left( {690 \times \frac{2}{6}} \right) - 7} \right] \cr & = {\text{Rs}}{\text{. }}223 \cr & {\text{C's share}} \cr & = {\text{Rs}}{\text{.}}\left[ {\left( {690 \times \frac{3}{6}} \right) - 9} \right] \cr & = {\text{Rs}}{\text{. }}336 \cr} $$
9
A box contains Rs. 56 in the form of coins of 1 rupee, 50 paise and 25 paise. The number of 50 paise coins is double the numbers of 25 paise coins and four times the number of one rupee coins. How many 50 paise coins are there in the box?
Discuss
Answer & Solution
Answer: Option B
Solution:
Total Amount = Rs. 56
Number of coins Ratio of 50 paise coin and 25 paise coins = 2 : 1
Number of coins Ratio of Rs. 1 coin and 50 paise coins = 1 : 4
∴ Number of coins Ratio of Rs. 1 : 50 paise : 25 paise = 1 : 4 : 2

Ratio of coin's value
Rs. 1 : 50 paise : 25 paise (value) = 1 : 2 : 0.50
(Multiply by 2 to remove the fraction value in above ratio)
i.e Rs. 1 : 50 paise : 25 paise (value) = 2 : 4 : 1
Value of 50 paise coin in Rs. 56 = $$\frac{4}{{7}} \times 56 = 32 $$
Number of 50 paise coin is = 32 × 2 = 64
10
Rs. 1740 is divided among A, B and C such that 0.5 of A = 0.6 of B = 0.75 of C. Then C will get = ?
Discuss
Answer & Solution
Answer: Option D
Solution:
$$\eqalign{ & \Rightarrow 0.5{\text{A}} = 0.6{\text{B}} = 1.75{\text{C}} \cr & \Rightarrow \frac{5}{{10}} \times {\text{A}} = \frac{6}{{10}} \times {\text{B}} = \frac{{75}}{{100}} \times {\text{C}} \cr & \Rightarrow \frac{1}{2}{\text{A}} = \frac{3}{5}{\text{B}} = \frac{3}{4}{\text{C}} \cr & \Rightarrow 10{\text{A}} = 12{\text{B }} = 15{\text{C}} \cr & \Rightarrow {\text{A}}\,\,\,\,\,\,\,:\,\,\,\,\,\,{\text{B}}\,\,\,\,\,\,\,\,\,:\,\,\,\,\,\,{\text{C}} \cr & 12 \times 15:10 \times 15:10 \times 12 \cr & \Rightarrow 180\,\,\,:\,\,\,\,\,150\,\,\,\,\,\,:\,\,\,\,120 \cr & \Rightarrow 6x\,\,\,\,\,\,:\,\,\,\,\,\,5x\,\,\,\,\,\,\,:\,\,\,\,\,4x \cr & {\text{Total}} = 6x + 5x + 4x = 15x \cr & 15x = 1740 \cr & \Rightarrow x = \frac{{1740}}{{15}} = {\text{Rs}}{\text{. }}116 \cr & \therefore {\text{Share of C is }}4x \cr & = 4 \times 116 \cr & = {\text{Rs}}{\text{. 464}} \cr} $$