Important Ratio And Proportion Problem Shortcut Tricks Type-2

Last updated on April 5th, 2023 at 12:25 pm

Ratio And Proportion Problem with solution and Shortcut Tricks for SSC, Bank PO, Railway, Lic Exam Type-2

Dear readers, In ratio and proportion problem Type-1 I have already discussed a basic concept, shortcut tricks of ratio and proportion problem and some important frequently asked questions so before reading another type of ratio and proportion problem you should have to read ratio and proportion type-1.

Now, Today we are going to discuss ratio and proportion problem type-2, 2.1, and 2.2. In this type, we will discuss some important shortcut tricks and frequently asked questions based on addition, difference, product and L.C.M & H.C.F. These questions will be very helpful for your upcoming all competitive exams like SSC, Bank PO, Railway, Lic etc.

Ratio And Proportion Problem with solution and Shortcut Tricks Type-2

(Q1)The product of two positive integers is 1575 and their ratio is 9:7. The smaller integer is.

दो संख्याओं का गुणनफल 1575 है और उनका अनुपात 9:7 है तो छोटी संख्या ज्ञात करें|

Solution:

Let the integers be 9x and 7x respectively

According to question

9x×7x = 1575

⇒ x² = 1575/63=25

⇒ x= 5

∴ smaller integer=7x=7×5=35 Ans.

(Q2)Three numbers are in the ratio of 3:2:5 and the sum of their squares are 1862. The smallest of these number is.

तीन संख्याओं का अनुपात 3:2:5 है और उनके वर्गो का योग 1862 है, तो सबसे छोटी संख्या ज्ञात करें|

Solution:

Let the number be 3x, 2x and 5x respectively

According to question

(3x)² + (2x)² + (5x)² = 1862

⇒38x²=1862

⇒x²=1862/38=49

⇒x = 7

∴ The smallest number=2x=2×7=14 Ans.

(Q3)The sum of three numbers is 116. The ratio of second to the third is 9:16 and the first to the third are 1:4. The second number is.

तीन संख्याओं का योग 116 है| दूसरी और तीसरी संख्या का अनुपात 9:16 और पहली और तीसरी संख्या का अनुपात 1:4 है, तो दूसरी संख्या ज्ञात करें|

Solution:

Therefore, the second number=(9/29)×116

                                             = 36 Ans.

(Q4)Of the three numbers, the ratio of the first and the second is 8:9 and that of the second and third is 3:4. If the product of the first and third number is 2400, then the second number is:

तीन संख्याओं में पहली और दूसरी संख्याओं का अनुपात 8:9 है और दूसरी व तीसरी का अनुपात 3:4 है| यदि पहली और तीसरी का गुणनफल 2400 है, तो दूसरी संख्या ज्ञात करें|

Solution:

Let the 1st, 2nd, and 3rd number be 8x, 9x, and 12x respectively

8x×12x=2400

⇒ x²=2400/96 = 25

⇒ x=5

2nd number=9x=9×5=45 Ans.

(Q5)what number should be added to each of 6, 14, 18 and 38 so that the resulting numbers make a proportion?

किस संख्या को 6, 14, 18, तथा 38 प्रत्येक में जोड़ा जाए की नई संख्याएँ समानुपातिक हो जाए|

Option: (1) 3  (2)  2  (3)  4   (4)  1

Solution:

Concept: if a, b, c, d are in proportion then a:b::c:d or a:b=c:d or a/b = c/d

Let x is added then

(6+x)/(14+x) = (18+x)/(38+x)

⇒ 228+38x+6x+x² = 252+14x+18x+x²

⇒ x²+44x+228 = x²+32x+252

⇒ 12x=24

∴x=2 Ans.

Second Method:

Let x is added then

(6+x)/(14+x) = (18+x)/(38+x)

put the value from option then

(6+2)/(14+2) = (18+2)/(38+2)

⇒ 8/16 = 20/40

⇒ 1/2 = 1/2

(Q6)Three numbers are in the ratio 3:4:5. The sum of the largest and the smallest equals the sum of the second and 52. the smallest number is.

तीन संख्याएँ 3:4:5 अनुपात में है| यदि सबसे बड़ी व सबसे छोटी संख्याओं का योग दूसरी संख्या व 52 के योग के बराबर है तो सबसे छोटी संख्या ज्ञात करें|

Solution:

Let the numbers be 3x, 4x and 5x

Now according to question

5x+3x = 4x+52

⇒ 4x=52

⇒ x=13

∴ Smallest number=3x=3×13=39 Ans.

(Q7)If the square of the sum of two numbers is equal to 4 times of their product, then the ratio of these numbers is:

किन्ही दो संख्याओं के योग का वर्ग, उनके गुणनफल के चार गुने के बराबर है, तो संख्याओं का अनुपात क्या है |

Solution:

Let the numbers are x and y

Now according to question

(X+y)² = 4xy

⇒ x² + y²+2xy = 4xy

⇒ x² + y²-2xy=0

⇒ (x-y)² = 0

so, x=y

∴ x:y=1:1 Ans.

(Q8)The sum of two numbers is equal to 20 and their difference is 25. The ratio of the two numbers is.

दो संख्याओं का योग 20 है और उनका अंतर 25 है तो संख्याओं का अनुपात ज्ञात करें|

Solution:

1st method: Shortcut

20+25 : 20-25

=45 : 5

=9 : 1 Ans.

2nd Method: General

Let the numbers are x and y

Now according to question

x+y = 25 ← (1)

x-y = 20 ← (2)

on adding Eqn.(1)and (2)

⇒ 2x= 45

⇒ x=22.5

put the value of x in Eqn.(1)

⇒ 22.5+y=25

y=2.5

∴ Required ratio=22.5:2.5 =9:1 Ans

(Q9)If A and B are in the ratio 4:5 and the difference of their squares is 81, what is the value of A?

यदि A तथा B 4:5 के अनुपात में है और उनके वर्गो का अंतर 81 है, तो A का मान ज्ञात करें|

Solution:

Let A=4x and B=5x

Now according to question

(5x)² – (4x)² = 81

⇒ 9x² =81

⇒ x² =81/9 = 9

⇒ x= 3

∴ A=4x=4×3=12 Ans.

Ratio And Proportion Problem with solution and Shortcut Tricks for SSC, Bank PO, Railway, Lic Exam Type-2.1

(Q1)The ratio of two numbers is 3:4 and their LCM is 120. The sum of numbers is.

दो संख्याएँ 3:4 के अनुपात में है और उनका लघुत्तम समापवर्त्य 120 है तो संख्याओं का योग ज्ञात करें|

Solution:

Let the numbers be 3x and 4x respectively.

LCM of 3x and 4x=12x

⇒ 12x=120

⇒ x=10

∴ Sum of the numbers=3x+4x=7x=7×10=70 Ans.

(Q2)The ratio of two numbers is 3:4 and their HCF is 15. Then the sum of the two numbers is:

दो संख्याएँ 3:4 के अनुपात में है और उनका महत्तम समापवर्त्य 15 है तो संख्याओं का योग ज्ञात करें|

Solution:

Let the numbers be 3x and 4x respectively.

HCF of 3x and 4x=x

⇒  x=15

∴ Sum of the two numbers=3x+4x=7x=7×15=105 Ans.

Ratio And Proportion Problem with solution and Shortcut Tricks for SSC, Bank PO, Railway, Lic Exam Type-2.2

(Q1)In a school having roll strength 286, the ratio of boys and girls is 8:5. If 22 more girls get admitted into the school, the ratio of boys and girls becomes.

286 छात्रों की एक स्कूल में लड़कों व लड़कियों का अनुपात 8:5 है| यदि 22 और लड़कीयाँ स्कूल में दाखिला लेती है तो लड़कों व लड़कियों का नया अनुपात ज्ञात करें |

Solution:

Let boys=8x and girls=5x

Now, According to the question

8x+5x=286

⇒ x= 286/13 =22

Boys=8×22=176

Girls=5×22=110

No. of girls at present after adding 22 girls=110+22=132

∴ Ratio=176/132=4:3 Ans.

Method-2

Initially number of boys=(8/8+5)×286=(8/13)×286=176

Number of girls=(5/13)×286=110

No. of girls at present after adding 22 girls=110+22=132

∴ Ratio=176/132=4:3 Ans.

(Q2)If there is a reduction in the number of workers in a factory in the ratio 15:11 and an increment in their wage in the ratio 22:25, then the ratio by which the total wage of the workers should be decreased is.

यदि एक कारखाने में मजदूरों की संख्या में 15:11 के अनुपात में कटौती हो और उनकी मजदूरी 22:25 के अनुपात में बढाई जाए तो उनकी कुल घटी हुई मजदूरी का अनुपात ज्ञात करें |

Solution:

(Q3)Two numbers are in the ratio 3:5. By adding 10 to each of them, the new numbers are in the ratio 5:7. Find the two numbers.

दो संख्याओ का अनुपात 3:5 है| यदि प्रत्येक संख्या में 10 जोड़ दी जाए तो उनका अनुपात 5:7 हो जाता है, तो संख्याएँ ज्ञात करें |

Solution: 1st Method: Shortcut

Now,

2 unit = 10

1 unit = 5

1st number=3×5=15

2nd number=5×5=25

Second Method: Shortcut

Now, cross multiply

(25-21)/7-5 = 4/2=2

Concept:[ 2 unit को 10 unit बनाना होगा क्योंकि question में दिया है 10 unit add किया जा रहा है |]

So, 2×5=10

1st number=3×5=15

2nd number=5×5=25

Third Method: General Method

Let the number be 3x and 5x

Now, According to the question

(3x+10)/(5x+10) = 5/7

⇒2x+70 = 25x+50

⇒4x=20

∴ x=5

1st number=3×5=15

2nd number=5×5=25

Important Note:जब difference same आएगा तब हमलोग इस type के question को method-1,2 and 3 किसी भी method से  solve कर सकते है पर यदि इस type के question में difference same नहीं आएगा तब हमलोग method-2 and 3 से solve करेंगे|

(Q4)What should be added to each term of the ratio 7:11, so as to make it equal to 3:4?

7:11 अनुपात की प्रत्येक संख्या में किस संख्या को जोड़ा जाए की अनुपात 3:4 हो जाए|

Solution: 1st Method: Shortcut

Now, cross multiply

(33-28)/4-3 = 5/1=5 Ans.

2 nd Method: General Method

Let the required number be x.

Now,

(7+x)/(11+x)= 3/4

⇒28+4x = 33+3x

⇒ x= 5 Ans.

(Q5)Two numbers are in the ratio 4:5 respectively. If each number is subtracted by 25, then the ratio becomes 3:4. Find the two numbers.

दो संख्याओ का अनुपात 4:5 है| यदि प्रत्येक संख्या में से 25 घटा दी जाए तो उनका अनुपात 3:4 हो जाता है, तो संख्याएँ ज्ञात करें |

Solution:1st Method: Shortcut

Now

1 unit = 25

1st number=4×25=100

2nd number=5×25=125

Second Method: Shortcut

Now, cross multiply

(16-15)/4-3 = 1/1=1

Concept:[ 1 unit को 25 unit बनाना होगा क्योंकि question में दिया है 25 unit subtract किया जा रहा है |]

So, 1×25=25

1st number=4×25=100

2nd number=5×25=125

Third Method: General Method

Let the number be 4x and 5x

Now, According to the question

(4x-25)/(5x-25) = 3/4

⇒16x-100 = 15x-75

⇒x=25

1st number=4×25=100

2nd number=5×25=125

Important Note:जब difference same आएगा तब हमलोग इस type के question को method-1,2 and 3 किसी भी method से  solve कर सकते है पर यदि इस type के question में difference same नहीं आएगा तब हमलोग method-2 and 3 से solve करेंगे|

(Q6)What number should be subtracted from both the terms of the ratio 11:15 so as to make it as 2:3?

11:15 अनुपात की संख्याओ में किस संख्या को घटाया जाए की अनुपात 2:3 हो जाए|

Solution:1st Method: Shortcut

Now, cross multiply

(33-30)/3-2 = 3/1=3 Ans.

2 nd Method: General Method

Let the required number be x.

Now,

(11-x)/(15-x)= 2/3

⇒33-3x = 30-2x

⇒ x= 3 Ans.

(Q7)The students in three classes are in the ratio 4:6:9. If 12 students are increased in each class, the ratio changes to 7:9:12. Then the total number of students in the three classes before the increase is.

तीन कक्षाओं में छात्रों का अनुपात 4:6:9 है | यदि प्रत्येक कक्षा में 12 छात्र बढ़ा दी जाए तो अनुपात 7:9:12 हो जाता है, तो शुरुआत में कुल कितने छात्र थे |

Solution:1st Method: Shortcut

Now,

3 unit=12

1 unit=4

Initially the number of students=19 unit=19×4=76 Ans.

2 nd Method: General Method

Let the original number of student be 4x, 6x, and 9x

Now,

(4x+12)/(6x+12)=7/9

⇒ 42x+84 = 36x+108

⇒ 6x= 24

⇒ x= 4

Initially the number of students=19x=19×4=76 Ans.

Important Note:जब difference same आएगा तब हमलोग इस type के question को method-1 and 2 किसी भी method से  solve कर सकते है पर यदि इस type के question में difference same नहीं आएगा तब हमलोग method-2 से solve करेंगे|

(Q8)The ratio between the boys and girls in a class is 6:5 respectively. If 8 more boys join the class and two girls leave the class then the respective ratio becomes 11:7. What is the number of boys in the class now?

एक कक्षा में लड़के व लड़कियों का अनुपात क्रमशः 6:5 है| यदि 8 और लड़के कक्षा में दाखिला लेता है एवं 2 लड़कीयाँ कक्षा छोड़ती है तो लड़के व लड़कियों का अनुपात 11 :7 हो जाता है तो अभी कक्षा में लडको कि संख्या क्या है |

Solution:

Let the number of boys and girls be 6x and 5x respectively.

According to the question,

(6x+8)/(5x-2) = 11/7

⇒42x+56=55x-22

⇒13x=78

⇒x=6

∴ Number of boys in the class=6x+8

=6×6+8=42 Ans.

Ratio and Proportion Problem with a solution and Shortcut Tricks for SSC CGL, Bank PO,  SSC CHSL, Railway Exam Type-1. In this type, I have already shared a Ratio and proportion Problem with a solution, Shortcut Tricks, Basic concept and frequently asked question if you have not read that yet, you should read it the right way here is the link.

Ratio and Proportion Type-1

Ratio and Proportion Part-3

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