161. 20% of the voters did not cast their vote in an election between two candidates. 10% of the votes polled were found invalid. The successful candidate got 56% of the valid votes and won by a majority of 1728 votes. The number of voters enrolled on the voters list was?

20% मतदाताओं ने दो उम्मीदवारों के बीच चुनाव में अपना वोट नहीं डाला। मतदान के 10% वोट अवैध पाए गए। सफल उम्मीदवार को 56% वोट मिले और 1728 वोट के बहुमत से जीत हासिल की। मतदाता सूची में दर्ज मतदाताओं की संख्या कितनी थी?

Option “D” is correct.

The successful candidate got 56% of the valid votes and won by a majority of 1728 votes.

(56 % – 44 %) of votes = 1728

12 % of votes = 1728

According to the question,

20 % voters didn’t cast their votes and 10 % of the votes are invalid. So,

= > (80/100)*(90/100)* total voters = 1728*(100/12)

= > Total voters = (1728*10*10*100) / (8*9*12) = 20000

162. In an election between two candidates, 30% votes declared invalid.  50% of total voters voted for the winner and the winner won by 600 votes. Find the total number of voters.

दो उम्मीदवारों के बीच एक चुनाव में, 30% वोट अवैध घोषित किए गए। कुल मतदाताओं में से 50% ने विजेता के लिए मतदान किया और विजेता ने 600 वोटों से जीत हासिल की। मतदाताओं की कुल संख्या ज्ञात कीजिये।

Option “C” is correct.

Let the total voter= 100x

Invalid votes = 30x

Valid votes= 70x

Winner’s vote= 50% of 100x = 50x

Loser’s vote = 70x -50x = 20x

(50-20) x = 30x

= > 30x = 600

x=20

= > 100*20 = 2000

163. In an election, there are only two candidates. Total 8000 votes are polled in the election. Out of them 25% votes are invalid. The winner won by 240 valid votes. Find the percentage of valid vote got by the loser.

एक चुनाव में, केवल दो उम्मीदवार होते हैं। चुनाव में कुल 8000 वोट पड़े। उनमें से 25% वोट अमान्य हैं। विजेता ने 240 वैध मतों से जीत दर्ज की। हारे हुए व्यक्ति को मिला वैध वोट का प्रतिशत ज्ञात कीजिये?

Option “D” is correct.

Number of valid votes = 75/100 x 8000 = 6000

Let, number of votes got by the loser = n

n + n + 240 = 6000

=> 2n = 6000 – 240

=> n = 5760/2

=> n = 2880

Required percentage = 2880/6000 x 100 = 48%

164. In an election in village, a total vote of the village is 10000 and 5% of the total votes are invalid. If the winning candidates got 55% of the valid votes, then what is the number of valid votes polled for other candidates?

गाँव में एक चुनाव में, गाँव का कुल मतदान 10000 होता है और कुल वोटों का 5% अवैध होता है। यदि विजयी उम्मीदवारों को वैध मतों का 55% मिला, तो अन्य उम्मीदवारों के लिए वैध मतों की संख्या कितनी है?

Option “A” is correct.

Number of valid votes = 10000 * 95/100 = 9500

Number of valid votes polled in other candidates = (100 – 55)/100 * 9500

= 4275

165. The number of girls in the school is 20% more than the number of boys in the same school in 2020. If the total number of students in the school in 2018 is 700 and the every year rate of the growth of the school is increased by 10%, then find the number of girls in the school in 2020?

2020 में स्कूल में लड़कियों की संख्या, उसी स्कूल में लड़कों की संख्या से 20% अधिक है। यदि 2018 में स्कूल में छात्रों की कुल संख्या 700 है और स्कूल की संख्या दर में प्रत्येक वर्ष में 10% से वृद्धि हुई है, फिर 2020 में स्कूल में लड़कियों की संख्या को ज्ञात कीजिए?

Option “A” is correct.

Total number of students in 2018 = 700

Total number of students in 2020 = 700 * 110/100 * 110/100 = 847

Number of girls to boys in 2020 = 120:100 = 6:5

Number of girls in 2020 = 6/11 * 847 = 462

166. The total number of students in team A is 25% more than that of team B and the total number of students in team C is 20% less than that of team B. If the difference between the total number of students in team A and C is 9, then find the total number of students in all the three teams?

टीम A में छात्रों की कुल संख्या, टीम B की तुलना में 25% अधिक है और टीम C में छात्रों की कुल संख्या, टीम B की तुलना में 20% कम है। यदि टीम A और C में छात्रों की कुल संख्या के बीच का अंतर 9 है, तो तीनों टीमों में छात्रों की कुल संख्या ज्ञात कीजिए?

Option “A” is correct.

The total number of students in team B = 4x

And the total number of students in team A = 4x * 125/100 = 5x

And the total number of students in team C = 4x * 80/100 = 3.2x

5x – 3.2x = 9

1.8x = 9

x = 5

The total number of students in all three students = (4 + 5 + 3.2) * 5 = 61

167. In a class number of girls are 150% more than boys. 14% of total girls are selected for Quiz contest and 21% of boys are selected for Quiz contest, then find the percentage of students those are not selected for quiz content?

एक वर्ग में लड़कियों की संख्या, लड़कों की संख्या से 150% अधिक हैक्विज़ प्रतियोगिता के लिए कुल लड़कियों में से 14% लड़कियों को चुना जाता है और 21% लड़कों को क्विज़ प्रतियोगिता के लिए चुना जाता है, फिर उन छात्रों का प्रतिशत ज्ञात करें जिन्हें क्विज़ प्रतियोगिता के लिए नहीं चुना गया है?

Option “C” is correct.

Let the total number of boys = 200a

Total number of girls = 250% of 200a = 500a

Number of girls selected in Quiz contest = 14% of 500a = 70a

Number of boys selected in Quiz contest = 21% of 200a = 42a

% of students selected in Quiz contest = [(70a + 42a) / (700a)]*100 = 16%

% of students not selected in Quiz contest = 100% – 16% = 84%

168. An admission of a school has increased in every academic year by 8%. If the number of students in the previous academic year is 2500, what is the number of students in the next year?

प्रत्येक शैक्षणिक वर्ष में एक स्कूल के प्रवेश में 8% की वृध्दि हुई है। यदि पिछले शैक्षणिक वर्ष में छात्रों की संख्या 2500 है, तो अगले वर्ष में छात्रों की संख्या कितना है?

Option “A” is correct.

 8% of 2500 = 8/100 x 2500 = 200

Total no. of students in the current year = 2500 + 200 = 2700

8% of 2700 = 216

So number of students in the next year = 2700 + 216 = 2916

Or

Short cut:

2500 * (108/100) * (108/100) = 2916

169. The total number of students in a college is 17,800. It has 65% boys and the rest are girls. If 40% of the boys and 60% of the girls do not have a smartphone, then find the total number of students who have smartphones.

एक कॉलेज में छात्रों की कुल संख्या 17,800 है। इसमें 65% लड़के हैं और बाकी लड़कियां हैं। यदि 40% लड़कों और 60% लड़कियों के पास स्मार्टफोन नहीं है, तो उन कुल छात्रों की संख्या ज्ञात करें जिनके पास स्मार्टफोन हैं।

Option “C” is correct.

Number of boys in the college = 17,800 × 65/100 = 11,570

Number of girls in the college = 17,800 × 35/100 = 6230

Now, the number of boys with smartphone = 11,570 × (100 – 40)/100

= 11,570 × 60/100

= 6942

And the number of girls with smartphone = 6230 × (100 – 60)/100

= 6230 × 40/100

= 2492

Thus, the total number of students who have smartphones,

= 6942 + 2492 => 9434

Hence, the required answer = 9434.

170. Monthly fees of a student in a school in 1200 rupees. If the fees per student becomes 900 rupees and total revenue of school is increased by 20%, find percentage increase in the number of students in a school.

एक स्कूल में एक छात्र की मासिक फीस 1200 रुपये है यदि प्रति छात्र की फीस 900 रुपये हो जाती है और स्कूल का कुल राजस्व 20% बढ़ जाता है, तो स्कूल में छात्रों की संख्या में प्रतिशत वृद्धि ज्ञात करें।

Option “C” is correct.

Revenue = fees per student x number of students

According to question

5/6 = 1200/900 x number of students

Number of students = 5/6 x 3/4 = 5/8   (ratio of initial and new students)

% change in number of students = 3/5 x 100 = 60%

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