Ratio and Proportion- Aptitude Questions and Answers - in Hindi

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In a bag, there are notes of 10, 20 and 50 in the ratio of 1 : 2 : 3. If the total money is 1000, how many notes of 10 are there?


एक बैग में, 10, 20 और 50 के नोट 1 : 2 : 3 के अनुपात में हैं। यदि कुल धन 1000 है, तो 10 के कितने नोट हैं।

A)
5

B)
10

C)
15

D)
30


Correct Answer :

5


Explanation :

Let the number of 10, 20 and 50 notes be X, 2X and 3X, respectively. Then ,
10*X + 40*X + 150*X = 1000
X = 5
So, the number of 10 notes are, X = 5

If A = B*(2/3) and B = C *(4/5), then what will be A: B: C ?


यदि A= B का 2/3 और B= C का 4/5 , तो A: B: C क्या होगा ?

A)
12:8:10

B)
15:10:8

C)
10:15:12

D)
8:12:15


Correct Answer :

8:12:15


Explanation :

A = B*(2/3) => A/B = 2/3
B = C *(4/5) => B/C = 4/5

So, A:B = 2:3 and B:C =4:5
Hence A:B:C =(2*4) :(3*4) :(3*5)
=8:12:15

If the annual income of A, B and C is in the ratio of 1: 3: 7 and the total annual income of A and C is 800000, then what is the monthly salary of B?


यदि A, B और C की वार्षिक आय 1: 3:7 के अनुपात में है और A तथा C की कुल वार्षिक आय 800000 है,तो B का मासिक वेतन है?

A)
20000

B)
25000

C)
30000

D)
15000


Correct Answer :

25000


Explanation :

Let the monthly salary of A, B and C are X, 3X and 7X, then

X+7x=800000
X=100000
Hence ,the monthly salary of B = 3*100000 / 12 => 25000

An examination of a school, the ratio of successful and unsuccessful candidates is 6: 1. If 6 more candidates are successful,then the ratio would be 9: 1 . What is the total number of candidates?


किसी स्कूल में एक परीक्षा में सफल और असफल परीक्षार्थियों का अनुपात 6:1 है। यदि 6 और परीक्षार्थी सफल हो जाते तो अनुपात 9 :1 होता ।परीक्षार्थियों की कुल संख्या है?

A)
140

B)
120

C)
200

D)
160


Correct Answer :

140


Explanation :

Let the successful candidates is 6X and unsuccessful candidates is X , then

Therefore, 6X+6 / X - 6 = 9/1
6X+6 = 9X- 54
3X=60
X=20
Hence , Total candidates= 6X+ X =7X
=> 7*20 =>140

The ratio between the two numbers is 4: 5. If 4 is increased in each numbers , then the ratio becomes 3: 5. What is the greater number?


दो संख्याओं के बीच का अनुपात 4:5 है। यदि प्रत्येक में 4 की वृद्धि कर दी जाए, तो अनुपात 3:5 हो जाता है। बड़ी संख्या है?

A)
36

B)
48

C)
56

D)
64


Correct Answer :

56


Explanation :

Let the numbers is 4X and 7X , then
4X+4 / 7X+ 4 = 3/5
20X+20 = 21X+12
X=8
Hence , greater number is= 7X=7*8 = 54

The ratio of two student numbers P and Q is 2: 5. If P's number is 120, then what is the Q's number?


दो छात्रों P और Q के अकों का अनुपात 2:5 है। यदि P के अंक 120 है, तो Q के अंक है?

A)
120

B)
240

C)
300

D)
360


Correct Answer :

300


Explanation :

Let the P's number is 2X and Q's number is 5X , then
2X = 120

Hence , Q's number = 5X=5*60 = 300

In a class of 49 students, the ratio of girls to boys is 4 : 3. If 4 girls leave the class, the ratio of girls to boys would be?


49 छात्रों की एक कक्षा में, लड़कियों व लड़कों का अनुपात 4: 3 है। यदि 4 लड़कियां कक्षा छोड़ देती हैं, तो लड़कियों व लड़कों का अनुपात क्या होगा?

A)

11 : 7


B)

8 : 7


C)

6 : 5


D)

9 : 8



Correct Answer :

8 : 7


Explanation :

Let the number of girls be 4x and boys be 3x.
4x + 3x =49
7x=49
x=7

So,number of girls, 4x = 4*7 = 28 and number of boys, 3x = 3*7 = 21

Now 4 girls leave thus number of girls = 28 - 4 = 24
Hence, new ratio of girls to boys = 24/21 = 8/7

The respective ratio betwen the monthly salary of Om and that of Pihu is 7 : 9. Om and Pihu, both save 20% and 40% out of their respective monhtly salary. Om invest 1/2 of his savings in PPF and Pihu invests 7/9 of his savings in PPF. If Om and Pihu together saved 17500 in PPF, what is Pihu’s monthly salary?


ओम और पिहु के मासिक वेतन का अनुपात 7: 9 है। ओम और पिहू, दोनों अपने मासिक वेतन में से 20% और 40% बचाते हैं। ओम अपनी बचत का 1/2 निवेश करता है और पिहू अपनी बचत का 7/9 हिस्सा, PPF में निवेश करते है। अगर ओम और पिहू ने मिलकर एक साथ PPF में 17500 रुपये निवेश करते हैं, तो पीहू का मासिक वेतन क्या है?

A)

72000


B)

36000


C)

45000


D)

40000



Correct Answer :

45000


Explanation :

Let,Om and Pihu monthly salary be7x
and 9x respectively.
Now, saving of Om = 7x* 20/100 =7x/5
and saving of Pihu = 9x* 40/100 =18x/5

Om’s investement in PPF=7x/5 * 1/2 =7x/10
and Pihu’s investment in PPF=18x/5 * 7/9 =14x/5

Now, according to the question,
7x/10 + 14x/5 = 17500
7x/10 + 28x/10 = 17500
35x/10 = 17500
x = 175000/35
x = 5000
Pihu’s monthly salary = 9x = 9 * 5000 = 45000

By increasing the price of entry ticket to a fair in the ratio 3 : 7, the number of visitors to the fair has decreased in the ratio 16 : 13. In what ratio has the total collection increased or decreased?


एक मेले में प्रवेश टिकट के मूल्य में 3: 7 के अनुपात में उचित वृद्धि करके, मेले में आने वाले आगंतुकों की संख्या 16: 13 के अनुपात में कम हो गई है। कुल संग्रह में किस अनुपात में वृद्धि या कमी हुई है?

A)

decreased in the ratio 91 : 48


B)

increased in the ratio 48 : 91


C)

increased in the ratio 39 : 112


D)

decreased in the ratio 112 : 39



Correct Answer :

increased in the ratio 48 : 91


Explanation :

Total collection = Price of each entry ticket * number of visitors
Increase in ratio = 16 * 3 : 13 * 7 = 48 : 91

If 2x=3y and 4y=5z, then what is x:z=?


यदि 2x = 3y और 4y = 5z, तो x: z = क्या है?

A)

3:4


B)

4:3


C)

15:8


D)

8:15



Correct Answer :

15:8


Explanation :

2x = 3y => x=3y/2

4y = 5z => z= 4y/5

Hence, x:z = (3y/2) : (4y/5) = 15:8

What quantity must be added to each term of the ratio a + b : a – b to make it equal to (a + b)2 : (a – b)2 ?


अनुपात (a + b) : (a - b) को (a + b) 2: (a - b) 2 के बराबर बनाने के लिए उसके पदो में कौन सी राशि जोड़ी जानी चाहिए?

A)

(a+b)/2a


B)

(b-1)/2a


C)

(b2 - a2 ) / 2a


D)

(a + b)/ (a – b)



Correct Answer :

(b2 - a2 ) / 2a


Explanation :

Let the X is quantity , then -
(a + b) + x / (a – b) + x = (a + b)2/(a – b)2
⇒ (a + b)(a – b)2 + (a – b)2.x = (a + b)2(a – b) + (a + b)2.x
⇒ (a + b)2.x - (a – b)2.x = (a + b)(a – b)2 - (a + b)2(a – b)
⇒ [a2 + b2 + 2ab - (a2 + b2 - 2ab )]x = (a + b)(a – b)(a – b) - (a + b)(a + b)(a – b)
⇒ [a2 + b2 + 2ab - (a2 + b2 - 2ab )]x = [ (a2 - b2)(a – b) – (a2 - b2) (a +b) ]
⇒ 4ab.x = (a2 - b2) [(a – b) – (a +b) ]
⇒ 4ab.x = -2b (a2 - b2)
⇒ x = (b2 - a2 ) / 2a

In a school 4/9 of the pupils are boys. There are 125 girls. How many boys are there?

A)

80


B)

100


C)

110


D)

120



Correct Answer :

100


Explanation :

Let total people be x
number of boys = 4x/9

So,number of girls = 1 - 4/9 = 5x/9
Then, 5x/9 = 125
x = 125* 9/5 = 25*9
x = 225 students

So number of boys = 4x/9 = 4/9 *225 = 100

If A:B = 3:4 and B:C = 5:6, find A:C?

A)

5:9


B)

3:4


C)

1:2


D)

5:8



Correct Answer :

5:8


Explanation :

As is given B/C = 5/6
Then, B = (5/6)*C
Substitute B value in A/B=3/4,
Then,
A/(5/6)*C = 3/4
A = (3/4)*(5/6)*C
A/C = (3/4)*(5/6)
A/C = 15/24
A/C = 5/8
So A : C = 5/8

IF X:Y = 3:4 AND Y:Z = 4:5, FIND X:Y:Z?

A)

2 : 3 : 4


B)

3 : 4 : 5


C)

4 : 5 : 6


D)

5 : 6 : 7



Correct Answer :

3 : 4 : 5


Explanation :

Given, X:Y = 3:4
X = 3Y / 4

Now, Y:Z = 4 : 5
5Y = 4Z
Z = 5Y / 4

So, X : Y : Z = 3Y / 4 : Y : 5Y / 4
= 3Y / 4 : 4Y / 4 : 5Y / 4
= 3Y : 4Y : 5Y
Therefore the ratio X:Y:Z = 3 : 4 : 5

Or

X : Y = 3 : 4 = 3*4:4*4 = 12/16
Y : Z = 4 : 5 = 4*4:5*4 = 16/20

Therefore the ratio X:Y:Z = 12:16:20 = 3:4:5

If A:B = 2:3 and B:C = 9:5 find A:B:C?

A)

2 : 3 : 4


B)

6: 9 : 5


C)

4 : 5 : 6


D)

5 : 6 : 7



Correct Answer :

6: 9 : 5


Explanation :

Given, A:B = 2:3
A=2B/3

Now, B:C = 9:5
5B=9C
C=5B/9

So, A:B:C = 2B/3 : B : 5B/9
= 9*2B/3 : 9*B : 9*5B/9
= 6: 9 : 5

Or

A:B = 2:3 = 2*9:3*9 = 18/27
B:C = 9:5 = 9*3:5*3 = 27/15

Therefore the ratio A:B:C = 18 : 27 : 15 = 6:9:5

If A:B = 3/5:5/7 and B:C = 3/4:2/5, find A:B:C?

A)

63:75:40


B)

65:75:80


C)

60:50:40


D)

60:70:80



Correct Answer :

63:75:40


Explanation :

A:B = 3/5:5/7 = 3*7:5*5 = 21 : 25
B:C = 3/4:2/5 = 3*5:4*2 = 15 : 8

Therefore for the ratio A:B:C

A:B = 21*15:25*15
B:C = 15*25:8*25

A:B:C =21*15 : 25*15 : 8*25
=21*3:25*3:8*5
=63:75:40

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