1. A sum fetched a simple interest of Rs. 5264 at a rate of 7 percent per year in 8 years. What is the sum?

एक राशि का 8 वर्षों में प्रति वर्ष 7 प्रतिशत की दर से 5264 रूपए का साधारण ब्याज है। राशि क्या है?


Option”A” is correct

SI = P × R × T/100

⇒ 5264 = P × 7 × 8/100

⇒ P = 5264 × 100/56

∴ P = Rs. 9400

2. A borrows a sum of Rs. 2,000 from his friend B on 31 December 2011 on the condition that he will return the same after one year with simple interest at 8% per annum. However, A gets into a position of returning the money on 1 July 2012. How much amount he has to return to B?

31 दिसंबर 2011 को A अपने दोस्त B से 2,000 रु. उधार इस शर्त पर लेता है कि वह उसे एक वर्ष बाद प्रतिवर्ष 8% साधारण ब्याज दर से लौटाएगा। हालांकि, A 1 जुलाई 2012 को राशि लौटाने की स्थिति में है। उसे B को कितनी राशि लौटानी है?


Option”B” is correct

Principal = 2000

Time = 6/12 = 1/2 years

Rate = 8%

Interest = (2000 × 8 × 1)/2 × 100 = 80

Amount = 2000 + 80 = Rs. 2080

3. A sum lent out at simple interest amounts to Rs. 6076 in 1 year and Rs. 7504 in 3 years. The sum and the rate of interest (approx) p.a are respectively:

साधारण ब्याज पर दी गयी एक धनराशि 1 वर्ष में 6076 रुपये और 3 वर्षों में 7504 रुपये हो जाती है। क्रमशः धनराशि और प्रतिवर्ष ब्याज की दर (लगभग) क्या है?


Option”D” is correct

Given that,

Sum lent out at simple interest to 6076 in 1 year and 7504 in 3 years.

SI of 2 years = 7504 – 6076 = 1428

SI of  1 year = 1428/2 = 714

Principal = 6076 – 714 = 5362

SI  = (P × R × T)/100

SI = (5362 × r × 1)/100

⇒ 714 = (5362 × r × 1)/100

⇒ r = 71400/5362 ≈ 13.32%

4. After 6 years, a sum invested at simple interest at the rate of r percent becomes twice of itself. What is the value of ‘r’?

r प्रतिशत की दर से साधारण ब्याज पर निवेश की गई राशि 6 वर्षों के बाद स्वयं का दो गुना हो जाती है। ‘r’ का मान क्या है? 


Option”B” is correct

Short trick:

Let the Principal be 100%.

SI will be after 6 years = 100%.

In 6 years total interest rate = 100%

In 1 year interest rate = 100/6 = (50/3) %

Detailed Solution:

Let principal be Rs. x

Amount = 2x

SI = 2x – x = x

Rate of interest = r

As we know,

SI = Prt/100

x = (x × r × 6)/100

r = 100/6 % = (50/3)%

5. Arun wants to pay Rs. 16000 cash for a colour television and Bala wants to purchase the same for Rs. 17776, due after 2 years. If the rate of simple interest is 5% per annum, which of the deals is better for the shopkeeper?

अरुन एक रंगीन टेलीविज़न के लिए 16000 रु. का नकद भुगतान करना चाहता है और 2 वर्षों के बाद, बाला उसी टेलीविज़न को 17776 रु. में खरीदना चाहता है। यदि साधारण ब्याज की दर 5% प्रति वर्ष है, तो दुकानदार के लिए कौनसा सौदा बेहतर है?


Option”D” is correct

Arun purchases the television = Rs. 16000

Price of the colour television = Rs. 16000

A = 17776, t = 2 years and r = 5%

As we know,

A – P = Prt/100

⇒ 17776 – P = (P × 2 × 5) /100

⇒ 17776 – P = P/10

⇒ 177760 – 10P = P

⇒ 10P + P = 177760

⇒ 11P = 177760

⇒ P = 177760/11

⇒ P = 16160

Television cost for Bala = 16160

In this deals of Bala better for the shopkeeper.

Short Trick

Let the TV cost be 100%

Interest rate for 2 year = 2 × 5 = 10%

110% = 17776

⇒ 100% = (17776/110) × 100 = 16160

6. A sum amounts to Rs. 56000 at the rate of 15% per annum simple interest for 4 years. What will be the interest on same sum at the rate of 12% per annum simple interest in triple the earlier time?

एक राशि 4 वर्ष के लिए 15% प्रति वर्ष की साधारण ब्याज की दर से 56000 रुपए हो जाती है। पहले से तिगुने समय में 12% प्रति वर्ष की साधारण ब्याज दर पर वही राशि का ब्याज क्या होगा?


Option”C” is correct

Let the sum be x

Interest = 56000 – x

⇒ 56000 – x = (x × 15 × 4) /100

⇒ 5600000 – 100x = 60x

⇒ 160x = 5600000

⇒ x = 35000

Now,

Interest on same sum at the rate of 12% per annum simple interest in triple the earlier time

New time = 3 × 4 = 12

⇒ Interest = (35000 × 12 × 12) /100

⇒ Interest = 50400

∴ Required interest is Rs. 50,400

7.The rate of simple interest on a sum of money is 5% p.a. for the first 4 years, 8% p.a. for the next 3 years and 10% p.a. for the period beyond 7 years. If the simple interest accumulated by the sum over a period of 10 years is Rs. 1,850, then the sum is:

किसी धनराशि पर साधारण ब्याज की दर पहले 4 वर्षों के लिए 5% प्रति वर्ष, अगले 3 वर्षों के लिए 8% प्रति वर्ष और 7 वर्षों से अधिक की अवधि के लिए 10% प्रति वर्ष है। यदि 10 वर्षों की अवधि में उस राशि पर अर्जित साधारण ब्याज 1,850 रुपये है, तो राशि है:


Option”C” is correct

Interest rate for first 4 years = 5%

Interest rate for next 3 years = 8%

Interest rate for next 3 years = 10%

Total simple interest for 10 years = Rs. 1850

As we know, SI = Prt/100

According to the question

(P × 5 × 4)/100 + (P × 8 × 3)/100 + (P × 10 × 3)/100 = 1850

⇒ 20P/100 + 24P/100 + 30P/100 = 1850

⇒ 74P = 185000

⇒ P = 185000/74

∴ P = Rs. 2500

Short Trick:

Let Principal be 100% and SI for 10 years = 1850

Total percentage of interest for 10 years = 4 × 5 + 3 × 8 + 3 × 10 = 74%

74% = 1850

⇒ 1% = 25

⇒ 100% = 2500

8. If in 13 years fixed sum doubles at simple interest, what will be the interest rate per year? (correct to two decimal places)

यदि 13 वर्षो में एक निश्चित राशि साधारण ब्याज पर दोगुनी हो जाती है, तो वार्षिक ब्याज की दर क्या होगी? (दो दशमलव स्थान तक लेने पर)


Option”A” is correct

Let P = x

⇒ A = 2x

SI = 2x – x = x

Time = 13 years

As we know,

SI = Prt/100

⇒ x = (x × r × 13)/100

⇒ r = 100/13

⇒ r = 7.69%

Short Trick:

Let P = 100%

SI for 13 years = 100%

Rate = 100/13 = 7.69%

9. Two equal amounts were borrowed at 5% and 4% simple interest. The total interest after 4 years amounted to Rs. 405. What was the total amount borrowed?

दो समान राशियाँ 5% और 4% की साधारण ब्याज दर पर उधार ली गई थीं। 4 वर्षों के बाद कुल ब्याज 405 रुपये हैं। कुल कितनी राशि उधार ली गई थी?


Option”C” is correct

Let the equal amount borrowed be Rs. ‘P’

Time = 4 years

∵ Simple interest = (Principal × Rate × Time)/100

Simple interest at 5% = (P × 5 × 4)/100 = Rs. 0.2P

Simple interest at 4% = (P × 4 × 4)/100 = Rs. 0.16P

⇒ Total interest after 4 years = 0.2P + 0.16P = Rs. 0.36P

But, total interest = Rs. 405

⇒ 0.36P = 405

⇒ P = 405/0.36 = Rs. 1125

∴ Amount borrowed = Rs. 1125

10. Seema invested a certain sum of money at the rate of interest 8% per annum for x years. If she got 2/5 of the principal as a simple interest, find the value of x?

सीमा ने x वर्ष के लिए 8% प्रति वर्ष ब्याज दर पर एक निश्चित राशि का निवेश किया। यदि उसे साधारण ब्याज के रूप में मूलधन का 2/5 हिस्सा प्राप्त होता है, तो x का मान ज्ञात कीजिए?


Option”C” is correct

Simple interest = (2/5) × principal

Simple interest : principal = 2 : 5

let ratio be a then SI = 2a and P = 5a

⇒ 2a = (5a × 8 × x)/100

⇒ x = 5 years

∴ The value of x is 5 years

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