91. A man spends 75% of his income. His income increases by 20% and his expenditure also increases by 10%, then the percentage increase in his savings is –

एक व्यक्ति अपनी आय का 75% खर्च करता है। उसकी आय में 20% की वृद्धि होती है और उनके खर्च में भी 10% की वृद्धि होती है, तो उसकी बचत में प्रतिशत वृद्धि है –


Option “D” is correct.

Calculation:

Let income of a man be 100 Rs.

Expenditure = 75 Rs.

Saving = 25 Rs.

New income = 100 × 120/100 = 120 Rs.

New expenditure = 75 × 110/100 = 82.5 Rs.

New saving = 120 – 82.5 = 37.5 Rs.

Percent increase in saving = [(37.5 – 25)/25] × 100

⇒ 12.5 × 4 = 50%

∴ The percentage increase in his savings is 50%.

92. In an election A got 39% of total votes and B got 15% of the total votes and C got the remaining votes. If the difference between the votes received by A and C was 56000. Find the total number of votes A received?

एक चुनाव में A को कुल मतों के 39% और B को कुल मतों के 15% और C को शेष मत प्राप्त होते हैं। यदि A और C को प्राप्त मतों का अंतर 56000 है, तो A को प्राप्त मतों की कुल संख्या ज्ञात कीजिए।

Option “D” is correct.

Given: In an election A got 39% of total votes and B got 15% of the total votes and C got the remaining votes. If the difference between the votes received by A and C was 56000.

Formula: If A got a% votes and B got b% votes, difference in the votes = (a – b) % of Total votes

Calculation:

Let total votes be 100x

A get = 39x

B = 15x

So, C gets  46x

As per question,

46x – 39x = 56000

⇒ 7x = 56000

⇒ X = 8000

Hence A gets = 39x = 39 × 8000 = 312000

93. If 90% of (a – b) is equal to 60% of (a + b), what percentage of a is b?

यदि (a – b) का 90%, (a + b) के 60% के बराबर है तो b, a का कितने प्रतिशत है?

Option “B” is correct.

Given:

90% of (a – b) = 60% of (a + b)

Formula used:

Percentage,(%)=ObtainedValue/MaximumValue×100Percentage,(%)=ObtainedValue/MaximumValue×100

Calculation:

90% of (a – b) = 60% of (a + b)

⇒ 90/100 × (a – b) = 60/100 × (a + b)

⇒ 9(a – b) = 6(a + b)

⇒ 9a – 9b = 6a + 6b

⇒ 3a = 15b

⇒ a = 5b

Now, (b/a) × 100

⇒ (b/5b) × 100 = 20%

∴ b is 20% of a

94. A sewing machine costs less than 15% every year. It was purchased 2 years ago. If the present value of the machine is Rs. 1445, find its cost price.

एक सिलाई मशीन का मूल्य हर वर्ष 15% की दर से कम होता है। इसे 2 वर्ष पहले खरीदा गया था। यदि मशीन का वर्तमान मूल्य 1445 रुपये है, तो इसका क्रय मूल्य ज्ञात कीजिये।

Option “D” is correct.

Given:

The present value of the machine is Rs. 1445. In every year cost less by 15% and it was purchased 2 years ago

Concept Used:

If the price of an article is p at present and it decreases at r% rate every year then after n year price of it will be p(1- r/100)n

Calculation:

Let the cost price be P

Time 2 years and cost less by 15% every year

The present price is 1445

P(1 – 15/100)2 = 1445

⇒ P × 85/100 × 85/100 = 1445

⇒ P = 1445 × 100/85 × 100/85

⇒ P = 2000

∴ Its cost price was Rs. 2000

95.A labour works 60 hours per week and earns Rs. 2400 as wages. If his per hour wages are increased by _________ percent and duration of work is decreased by _________  percent then his income decreases by 1%.

Which of the following options satisfies the two blanks in the question?

A. 10, 10

B. 15, 12.5

C. 20, 17.5

D. 25, 20.8

Option “D” is correct.

Per hour wages = 2400/60 = Rs. 40

Duration of work = 60 hours

Since there is 1% decrease in the income:

∴ New income should be = 2400 × 0.99 = Rs. 2376

Using the options:

A. 10% increment in wages per hour and 10% decrement in time duration.

∴ New income = 40 × 1.1 × 60 × 0.9 = Rs. 2376

Hence, option A is correct.

 B. 15% increment in wages per hour and 12.5% decrement in time duration.

∴ New income = 40 × 1.15 × 60 × 0.875 = Rs. 2415

Hence, option B is not correct.

C. 20% increment in wages per hour and 17.5% decrement in time duration.

∴ New income = 40 × 1.2 × 60 × 0.825 = Rs. 2376

Hence, option C is correct.

D. 25% increment in wages per hour and 20.8% decrement in time duration.

∴ New income = 40 × 1.25 × 60 × 0.792 = Rs. 2376

Hence, option D is correct.

Hence, A, C and D are correct.

96. The average income of 12 peons is Rs. 10000 and the average income of 6 nurses is Rs. 8000. if there is an increase in the salary of each peon by 5% and the salary of each nurse by 8% then what is the percentage change in total salary of 12 peons and 6 nurses?

12 चपरासियों की औसत आय 10000 रुपए है तथा 6 नर्सों की औसत आय 8000 रुपए है। यदि प्रत्येक चपरासी की आय में 5% से वृद्धि होती है और प्रत्येक नर्स की आय में 8% से वृद्धि होती है तो 12 चपरासियों और 6 नर्सों की कुल आय में प्रतिशत परिवर्तन क्या है?

Option “D” is correct.

Given,

Average income of 12 peons = Rs. 10000

Salary of a peon = Rs. 10000

Salary of 12 peons = 10000 × 12 = 120000

Average income of 6 nurses = Rs. 8000

Salary of a nurse = Rs. 8000

Salary of 6 nurse = 8000 × 6 = 48000

Total salary of 12 peons and 6 nurses before increment = 120000 + 48000 = 168000

Salary of a peon after increment = 10000 + 10000 × 5/100 = 10500

Salary of a nurse after increment = 8000 + 8000 × 8/100 = 8640

Total salary of 12 peons and 6 nurses after increment = 10500 × 12 + 8640 × 6 = 177840

Percentage change in salaries of 12 peons and 6 nurses

= [(177840 – 168000)/168000] × 100 = 5.85%

∴ Percentage change in salaries of 12 peons and 6 nurses is 5.85%.

97. The price of a unit in electricity bills is increased by 2%. Approximately by what percent person should reduce his consumption so as not to increase his monthly expenditure?

बिजली के बिल में एक इकाई की कीमत 2% से बढ़ जाती है। एक व्यक्ति को लगभग कितने प्रतिशत से अपनी खपत घटानी चाहिए ताकि उसके मासिक व्यय में वृद्धि न हो?

Option “C” is correct.

Let Old price of a unit in electricity bill be Rs. A.

Given,

Price of a unit is increased by 2%.

New price of electricity unit = A + A × 2/100 = 51A/50

Let consumption of units at old price be C units.

Consumption of units at new price is M% of Old unit = (M/100) × C

As known,

Expenditure = Price × units

To keep expenditure same,

⇒ A × C = 51A/50 × (MC/100)

⇒ 5000 = 51M

⇒ M = 98.03

Consumption units at new electricity unit price is 98.03%.

Consumption is reduced by 100 – 98.03 = 1.97% ~ 2%

∴ To maintain expenditure constant electricity units consumption should be reduced by 2%.

98. There were two candidates in an election, 10% voters did not cast their vote and 48 votes were found invalid. The winning candidate got 53% of the total votes and won by 304 votes. Find the total number of votes enrolled.

एक चुनाव में दो उम्मीदवार थे, 10% मतदाता अपना मतदान नहीं करते हैं और 48 मत अमान्य पाए जाते हैं। विजेता उम्मीदवार ने दिए गए कुल मतों का 53% मत प्राप्त किये और 304 मतों से विजयी हुआ। डाले गए कुल मतों की संख्या ज्ञात कीजिये।

Option “D” is correct.

Given:

10% voters did not cast their votes 

Total invalid votes = 48 

The winning candidate got 53% of the total votes 

Total winning votes = 304 

Calculations:

Let the total number of voters be 100x 

Total number of votes who cast their votes = 100x × 90/100 = 90x 

Total number of valid votes = 90x – 48 

Votes gained by winner candidate = 100x × 53/100 = 53x 

Votes gained by loser candidate = 90x – 48 – 53x = 37x – 48

Winning votes = Winner votes – Loser votes 

⇒ 304 = 53x – (37x – 48)

⇒ 304 = 53x – 37x + 48 

⇒ 16x = 256 

⇒ x = 16 

The total number of voters = 100x = 1600

∴ The total number of votes is 1600

99. In a college exam, 43 passed in accounts, 42 passed in digital marketing and 40 passed in social science. In all the three exams, 10 got passing marks. 22 passed accounts and digital marketing, 23 passed in accounts and social science, 16 passed in digital marketing and social science. Find how much percentage of the students passed only in two subjects to students passed only in one subject.

एक कॉलेज की परीक्षा में, 43 अकाउंट्स में उत्तीर्ण हुए, 42 डिजिटल मार्केटिंग में उत्तीर्ण हुए और 40 सामाजिक विज्ञान में उत्तीर्ण हुए हैं। सभी तीन परीक्षाओं में 10 को उत्तीर्ण अंक प्राप्त हुए हैं। 22 अकाउंट्स और डिजिटल मार्केटिंग में उत्तीर्ण हुए, 23 अकाउंट्स और सामाजिक विज्ञान में उत्तीर्ण हुए, 16 डिजिटल मार्केटिंग और सामाजिक विज्ञान में उत्तीर्ण हुए हैं। एक विषय मे उत्तीर्ण छात्रों की संख्या की तुलना मे केवल दो विषयों मे उत्तीर्ण छात्रों की संख्या का प्रतिशत ज्ञात कीजिये।

Option “A” is correct.

We can make this diagram from the information

Required percentage

⇒ [(13 + 12 + 6)/(8 + 14 + 11)] × 100 = 93.93%

100. A number increased by 16.66% , 14.28% , 9.09% and 11.11% respectively and after it decreased by 12.5% , 8.33%, 14.28% and 10% respectively. Find the total change in percentage.

एक संख्या में क्रमशः 16.66%, 14.28%, 9.09% और 11.11% की वृद्धि होती है और इसके बाद क्रमशः 12.5%, 8.33%, 14.28% और 10% की कमी होती है। प्रतिशत में कुल परिवर्तन ज्ञात कीजिये।

Option “D” is correct.

Concept:

16.66% = 1/6

14.28% = 1/7

9.09% = 1/11

11.11% = 1/9

12.5% = 1/8

8.33% =1/12

14.28% = 1/7

10% = 1/10

Calculation:

Let the number be x

Then, If it is increased by 16.66% i.e 1/6

⇒ x × ((6 + 1)/6)

⇒ x × (7/6)

Similarly, if it is decreased by 12.5% i.e 1/8 

⇒ x × ((8 – 1)/8)

⇒ x × (7/8)

Now, we will use all other percentages in ratio form as –

∴ The number increased by = x × 7/6 × 8/7 × 12/11 × 10/9 × 7/8 × 11/12 × 6/7 × 9/10

⇒ x

∴ There is no overall change in the percentage.

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