Ratio & Proportion Tips along with Practice Questions & Solutions for Bank Exams

Major banking exams including SBI PO & RBI Assistant Prelims are on its way and many aspirants find quant a difficult section to prepare. To make your quant preparation easy we are providing a few tips and practice questions along with solutions for all important topics. This blog talks about Ratio & Proportion Tips along with Practice Questions & Solutions for Bank Exams. These practice questions are for prelims exams and are combined with solutions so as to have a better understanding by all the aspirants preparing for the upcoming exams including SBI PO prelims and RBI Assistant prelims. Mentioned below are a few tips and tricks as to how to go about solving ratio and proportion questions followed by their solutions.

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and Proportion Tips

1.  Ratio: The ratio of two quantities ‘a’ and ‘b’, in the same units, is the fraction (a/b) and we write it as a:b.

2. Proportion: The equality of two ratios is called proportion.

If a:b = c:d, we write, a:b::c:d and we say that ‘a’, ‘b’, ‘c’, ‘d’ are in proportion. Here ‘a’ and ‘d’ are called extremes, while ‘b’ and ‘c’ are called mean terms. Also, Product of means = Product of extremes.

Thus, a:b::c:d = (b × c) = (a × d)

3. Third Proportional: If a:b = b:c, then ‘c’ is called the third proportional to ‘a’ and ‘b’.

4. Fourth Proportional: If a:b = c:d, then ‘d’ is called the fourth proportional to ‘a’, ‘b’ and ‘c’.

5. Mean Proportional: Mean proportional between ‘a’ and ‘b’ is √ab.

6. If a > b and ‘x’ is a positive quantity, then (a/b) > {(a + x)/(b + x)} and (a/b) < {(a – x)/(b – x)}

7. If a < b and ‘x’ is a positive quantity, then (a/b) < {(a + x)/(b + x)} and (a/b) > {(a – x)/(b – x)}

8. If (a/b) = (c/d) = (e/f) = k, then:

i. {(a + c + e)/(b + d + f)} = k

ii. {(pa + qc + re)/(pb + qd + rf)} = k, where all ‘p’, ‘q’ and ‘r’ are either positive or negative real numbers.

Probability Tips & Practice Questions for SBI PO Prelims

Ratio & Proportion Tips along with Practice Questions & Solutions for Bank Exams

Question 1: The ratio of number of apples sold by Mohan to that of Sohan was 8:5, respectively. Munna sold (27/40) of number of apples sold by Mohan. If number of apples sold by Sohan was 1250 then find the number of apples sold by Munna.  

A) 1250

B) 1350

C) 1450

D) 1500

E) 1680

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Question 2: The ratio of male and female in a town with population 6240 is 5:3, respectively. If 510 females joined the village, the ratio of male and female in village becomes 26:x, find the value of (32 – x).

A) 5

B) 9

C) 13

D) 19

E) 24

Question 3: Kunti decided to distribute 1260 coins among her three sons, Arjun, Bhim, and Yudhishthir in the ratio of 2:3:4, respectively but mistakenly, she distributed the coins in the ratio of 2:3:x, andthus Yudhishthir got 200 coins less than he was supposed to receive. Find the value of ‘x’.

A) 1

B) 2

C) 3

D) 4

E) 5

Question 4: In a company, the ratio of the male to female employees is 7:9 and the ratio of the graduates to post graduates employees is 4:5. Find the total number of employees if the difference between the number of male employees and the number of graduate employees is 2.

A) 288

B) 264

C) 250

D) 294

E) 312

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Question 5: A shopkeeper sold a total 800 mobiles and laptops in the ratio of 13:19, respectively. If the number of earphones sold by the shopkeeper is 100 less than that of mobiles sold, then find the ratio of number of earphones to the number laptops sold.

A) 5:13

B) 7:19

C) 9:19

D) 8:13

E) 4:5

Question 6: The ratio of waitlisted to RAC ticket booked in a train is 9:5, respectively. The number of confirmed ticket booked is 25% more than the difference of RAC and waitlisted tickets booked. If the sum of the given three types of tickets booked is 6650, then find the sum of RAC and confirmed tickets booked.

A) 3500

B) 3200

C) 4000

D) 2800

E) 4200

Question 7: The ratio of the number of laptops and mobiles sold by a shopkeeper is 5:7, respectively. The ratio of total number of laptops to that of mobiles the shopkeeper had is 9:8. If the number of unsold laptops and mobiles is 105 and 55, respectively, then find the ratio of sold to unsold number of laptops.

A) 3:7

B) 1:4

C) 2:9

D) 5:7

E) 3:8

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Question 8: A bag contains 32 red balls and 48 blue balls. Some balls were taken out of the bag such that the ratio of blue to red balls in the bag becomes 16:9. If the number of blue balls drawn is 2 more than that of the red balls, then find the total number of balls drawn from the bag.

A) 30

B) 24

C) 36

D) 12

E) 18

Question 9: Company B has 25% more employees than Company A. The respective ratio of males to females in Company A is 4:3. The ratio of males to females in Company B is 7:5. If number of males in Company A is 1920, then find the difference between number of females in Company A and that in Company B.

A) 320

B) 350

C) 310

D) 280

E) 240

Question 10: Daksh spends his pocket money on only four items in the ratio 5:8:2:3, respectively. The difference between his highest and lowest spending is Rs. 900. If he saves Rs. 900 then find the total pocket money received by him.

A) Rs. 3600

B) Rs. 3000

C) Rs. 2400

D) Rs. 4200

E) Rs. 4000

प्रश्न 1: Mohan और Sohan द्वारा बेचे गए apples की संख्या का अनुपात क्रमशः 8: 5 था। Munna द्वारा बेचीं गई apples की संख्या Mohan द्वारा बेचे गए apples की संख्या का (27/40) थी। यदि Sohan द्वारा बेची गई apples की संख्या 1250 थी तो Munna द्वारा बेची गई apples की संख्या ज्ञात करें ?

A) 1250

B) 1350

C) 1450

D) 1500

E) 1680

प्रश्न 2: 6240 जनसंख्या वाले एक शहर में पुरुष और महिला का अनुपात क्रमशः 5: 3 है। यदि 510 महिलाएं गांव में शामिल हो गईं, तो गांव में पुरुष और महिला का अनुपात 26: x हो जाता है, (32 – x) का मान ज्ञात करें ?

A) 5

B) 9

C) 13

D) 19

E) 24

प्रश्न 3: कुंती ने अपने तीन पुत्रों, अर्जुन, भीम और युधिष्ठिर के बीच क्रमशः 2:3:4 के अनुपात में 1260 सिक्के वितरित करने का निर्णय लिया, लेकिन गलती से, उन्होंने सिक्कों को 2:3:x के अनुपात में वितरित कर दिया, और इस प्रकार युधिष्ठिर को जितना मिलना चाहिए था उससे 200 सिक्के कम मिले। ‘x’ का मान ज्ञात करें’।

A) 1

B) 2

C) 3

D) 4

E) 5

प्रश्न 4: एक कंपनी में, पुरुष और महिला कर्मचारियों का अनुपात 7: 9 है और स्नातकों और पोस्ट ग्रेजुएट कर्मचारियों का अनुपात 4: 5 है।यदि पुरुष कर्मचारियों की संख्या और स्नातक कर्मचारियों की संख्या के बीच का अंतर 2 है, तो कर्मचारियों की कुल संख्या ज्ञात करें?

A) 288

B) 264

C) 250

D) 294

E) 312

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प्रश्न 5: एक दुकानदार ने कुल 800 mobiles और laptops को क्रमशः 13:19 के अनुपात में बेचा।यदि दुकानदार द्वारा बेचे गए earphones की संख्या बेचे गए mobiles की तुलना में 100 कम है, तो बेचे गये earphones और laptops की संख्या का अनुपात ज्ञात करें?

A) 5:13

B) 7:19

C) 9:19

D) 8:13

E) 4:5

प्रश्न 6: एक ट्रेन में बुक किए गए waitlisted और RAC टिकट का अनुपात क्रमशः 9: 5 है।बुक किए गए कन्फर्म टिकट की संख्या बुक किए गए RAC और waitlisted टिकटों के अंतर से 25% अधिक है।यदि दिए गए तीन प्रकार के टिकटों का योग 6650 है, तो बुक किए गए RAC और कन्फर्म टिकटों का योग ज्ञात करें?

A) 3500

B) 3200

C) 4000

D) 2800

E) 4200

प्रश्न 7: एक दुकानदार द्वारा बेचे जाने वाले लैपटॉप और मोबाइल की संख्या का अनुपात क्रमशः 5: 7 है।दुकानदार के पास लैपटॉप और मोबाइल की कुल संख्या का अनुपात 9: 8 है।यदि नहीं बिकने वाले लैपटॉप और मोबाइल की संख्या क्रमशः 105 और 55 है, तो बेचे गए और नहीं बेचे गए लैपटॉप की संख्या का अनुपात ज्ञात करें?

A) 3:7

B) 1:4

C) 2:9

D) 5:7

E) 3:8

प्रश्न 8: एक बैग में 32 red balls और 48 blue balls होती हैं।कुछ balls को बैग से बाहर निकाल दिया गया था जिससे बैग में blue और red balls का अनुपात 16: 9 हो जाता है।यदि निकाले गए blue balls की संख्या निकाले गए red balls की तुलना में 2 अधिक है, तो बैग से निकाले गए balls की कुल संख्या ज्ञात करें?

A) 30

B) 24

C) 36

D) 12

E) 18

प्रश्न 9: Company A की तुलना में Company B में 25% अधिक कर्मचारी हैं। Company A में पुरुषों और महिलाओं का संबंधित अनुपात 4: 3 है। Company B में पुरुषों और महिलाओं का अनुपात 7: 5 है। यदि Company A में पुरुषों की संख्या 1920 है, तो Company A और Company B में महिलाओं की संख्या के बीच का अंतर ज्ञात करें?

A) 320

B) 350

C) 310

D) 280

E) 240

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प्रश्न 10: Daksh अपने जेबखर्च को केवल चार वस्तुओं पर क्रमशः 5: 8: 2: 3 के अनुपात में खर्च करता है।उनके उच्चतम और न्यूनतम खर्च के बीच का अंतर Rs. 900 है|यदि वह Rs. 900 बचाता है फिर उसके द्वारा प्राप्त कुल जेबखर्च ज्ञात करें?

A) Rs. 3600

B) Rs. 3000

C) Rs. 2400

D) Rs. 4200

E) Rs. 4000

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ANSWER KEYS and SOLUTIONS:

Solution 1: B)

Number of apples sold by Mohan = 1250/5 × 8 = 2000

Number of apples sold by Munna = 27/40 × 2000 = 1350

Hence, option b.

Solution 2: C)

Number of males in village = {5/(5 + 3)} × 6240 = 3900

Number of females in village = {3/(5 + 3)} × 6240 = 2340

According to question,

3900: (2340 + 510) = 26: x

3900: 2850 = 26: x

150: 2850 = 1: x

x = 2850/150, x = 19

So, (32 – x) = 32 – 19 = 13

Hence, option c.

Solution 3: B)

Coins received by Yudhishthir in first case = (4/(2 + 3 + 4)) × 1260 = 560

Coins received by Yudhishthir mistakenly = (x/(2 + 3 + x)) × 1260

According to question,

(x/(2 + 3 + x)) × 1260 = 560 – 200

1260x = 360(5 + x)

1260x = 360x + 1800

1260x – 360x = 1800

x = 1800/900 = 2

Hence, option b.

Solution 4: A)

Let the total employees = x

According to the question,

x × 4/9 – x × 7/16 = 2

(64x – 63x)/144 = 2

x = 288

Hence, option a.

Solution 5: C)

Number of mobiles sold = 800 × 13/32 = 325

Number of laptops sold = 800 – 325 = 475

Therefore, number of earphones sold = 325 – 100 = 225

Required ratio = 225:475 = 9:19

Hence, option c.

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Solution 6: A)

Let the number of waitlisted and RAC tickets booked be 9x and 5x respectively.

Therefore, number of confirmed tickets booked = 1.25(9x – 5x) = 5x

According to the question,

5x + 5x + 9x = 6650

Or, x = 6650/19 = 350

Required sum = (5x + 5x) = 10x = 3500

Hence, option a.

Solution 7: D)

Let the total number of laptops and mobiles be 9x and 8x respectively.

And the number of laptops and mobiles sold be 5y and 7y respectively.

According to the question,

9x – 5y = 105…… (1)

8x – 7y = 55……. (2)

On solving equation (1) and (2), we get x = 20 and y = 15

Required ratio = 5y/105 = 5:7

Hence, option d.

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Solution 8: A)

Let the number of blue balls drawn be ‘x’

Therefore, number of red balls drawn = (x – 2)

According to the question,

(48 – x)/(32 – x + 2) = 16/9

Or, 432 – 9x = 544 – 16x

Or, 7x = 112

Or, x = 16

Therefore, total number of balls drawn = x + x – 2 = 2x – 2 = 30 balls

Hence, option a.

Solution 9: C)

Number of males in Company A = 1920

Number of females in Company A = 1920 × (3/4) = 1440

Total number of employees in Company A = 1920 + 1440 = 3360

Total number of employees in Company B = 1.25 × 3360 = 4200

Number of females in Company B = 4200 × (5/12) = 1750

Required difference = 1750 – 1440 = 310

Hence, option c.

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Solution 10: A)

Let the amount spent by Daksh on four items be Rs. 5x, Rs. 8x, Rs. 2x and Rs. 3x, respectively

According to the question,

8x – 2x = 900

Or, x = 900/6 = 150

Pocket money received by Daksh = (5x + 8x + 2x + 3x) + 900 = Rs. 3600

Hence, option a.

This brings us to the end of the article. Prepare well for ratio and proportion topic by following the above mentioned strategy & tips and by practicing the questions given here.

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