51. The side of a square is increased by P% then find % change in its area?

एक वर्ग की भुजा में P% की वृद्धि की जाती है, तो इसके क्षेत्रफल में % परिवर्तन ज्ञात कीजिए।

Option “B” is correct.

Let P = 20% = 1/5

Side original = 5 and increased side = 6

Original area = 25

New area = 36

Percentage change in area = (36 – 25)/25] × 100

11 × 4 = 44%

Check by options

(3) – [2P + (P/10)2]

[2 × 20 + (20/10)2] = 44%

Hence option (2) is correct

52. Two number are 40% and 30% less than the third number. If the fourth number is 7.5 which is one fourth of the first number, then find the third number.

तीसरी संख्या की तुलना में दो संख्या 40% और 30% कम है। यदि चौथी संख्या 7.5 है जो पहली संख्या की एक चौथाई है, तो तीसरी संख्या ज्ञात कीजिए।

Option “C” is correct.

Let the third number be 100x.

∴ The first number will be 60x and the second number will be 70x.

∴ The fourth number will be = 60x × 1/4 = 15x

As we know fourth number = 7.5

⇒ 15x = 7.5

⇒ x = 1/2

∴ Third number = 100 × 1/2 = 50

53. A is 25% more than the B while C is 11.11% more than the sum of A and B, then by what percent of C is more than the A?

A, B से 25% अधिक है जबकि C, A और B के योग से 11.11% अधिक है, तो C, A से कितने प्रतिशत अधिक है?

Option “B” is correct.

Let the value of B be 100.

Value of A = 100 × 125/100 = 125

Value of C = (A + B) × 10/9 = (125 + 100) × 10/9 = 225 × 10/9 = 250

∴ Required Percentage = [(250 – 125)/125] × 100 = 100%

54. Anu spends 90% of her income. If her expenditure increase by 25% and saving increase by 30%, then by what percent does her salary increase?

अनु अपनी आय का 90% व्यय करती है। यदि उसका व्यय 25% बढ़ता है और बचत में 30% की वृद्धि होती है, तो उसके वेतन में कितने प्रतिशत की वृद्धि हुई है?

Option “D” is correct.

Let the total income of Anu = 100

Expenditure = 90 × 100/100 = 90

Saving = 100 – 90 = 10

Now, Expenditure = 90 × 125/100 = 112.5

Saving = 10 × 130/100 = 13

⇒ 112.5 + 13 = 125.5o

Required percentage = 25.5 × 100/100 = 25.5%

55. If the price of tea is increased by 12.5%, find how much percent must a house holder reduce her consumption of tea by, so as not to increase the expenditure.

यदि चाय की कीमत 12.5% बढ़ जाती है, तो ज्ञात कीजिए कि एक गृहस्थ को अपने चाय की खपत में कितने प्रतिशत की कमी करनी चाहिए जिससे व्यय में वृद्धि ना हो?

Option “A” is correct.

After the price of tea is increased by 12.5%, the ratio of the increased price and old price will be 9/8.

Since, Expenditure = price × consumption

∴ Ratio of the reduced consumption and old consumption is 8/9.

Percentage decrease in the consumption = (decrease in consumption/old consumption) × 100

= (1/9) × 100 = 11 1/9%

56. Two numbers are 15% and 27% lesser than a third number. By how much percent is the second number to be enhanced to make it equal to the first number?

दो संख्याएँ तीसरी संख्या से 15% और 27% कम हैं। तो दूसरी संख्या को पहली संख्या के बराबर बनाने के लिए इसे कितना प्रतिशत बढ़ाया जाना चाहिए।


Option “C” is correct.

Given:

Two numbers are 15% and 27% lesser than a third number.

Formula used:

Required percentage = [(First number – Second number)/Second number] × 100

Calculation:

Let the third number be 100

Then first number = 100 – 15 = 85

Second number = 100 – 27 = 73

Required percentage = [(85 – 73)/73] × 100

⇒ (12/73) × 100

⇒ 1200/73

∴ Required percentage 16.44%

57. The sum of the two number is 80% more than the greater number. If the smaller number is 40. By what per cent, the greater number is greater than the smaller number?

दो संख्याओं का योगफल बड़ी संख्या से 80% अधिक है। यदि छोटी संख्या 40 है, तो बड़ी संख्या, छोटी संख्या से कितने प्रतिशत अधिक है?


Option “A” is correct.

Let the greater number is greater than the smaller number by x.

According to the question

⇒ x + 40 = x × (180/100)

⇒ (180x/100) – x = 40

⇒ 80x/100 = 40

⇒ x = 40 × (100/80)

⇒ x = 50

The greater number is greater than the larger than that of smaller number by = [(50 – 40)/40] × 100 = 25%

58. What is the ratio of two successive increases of 5% each to two successive discounts of 6% each?

5% प्रत्येक की दो क्रमिक वृद्धि का 6% प्रत्येक की दो क्रमिक छूट से अनुपात क्या है?

Option “D” is correct.

As we know,

 two successive increase of 5% each = 5 + 5 + (5 × 5)/100 = 10 + 0.25 = 10.25%

 two successive discount of 6% each = 6 + 6 – (6 × 6)/100 = 12 – 0.36 = 11.64%

Required ratio = 10.25 ∶ 11.64 = 1025 ∶ 1164 

59. A is 40% less than B, and C is 40% of the sum of A and B. The difference between A and B is what percentage of C?

A, B से 40% कम है और C A और B के योगफल का 40% है। A और B के बीच अंतर C का कितना प्रतिशत है?

Option “C” is correct.

Let the value of B be 100.

Value of A = 100 × (60/100) = 60

Value of C = (60 + 100) × (40/100) = 64

Required difference = [(100 – 60)/64] × 100 = 62.5%

60. If 40% of x equal 50% of y, then find the value of y : x.

यदि x का 40%, y के 50% के बराबर है, तब y : x का मान ज्ञात कीजिये। 

Option “C” is correct.

Given:

40% of x equal 50% of y

Solution:

40% of x equal 50% of y

⇒ 40/100 × x = 50/100 × y

⇒ 4x = 5y

∴ y : x = 4 : 5

 

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