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Class 10 (Madhyamik)
Mathematics
Compound Interest and Uniform Rate of Increase or Decrease (Set 01 (Foundation Level))

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West Bengal Board (WBBSE) Class 10 (Madhyamik) Mathematics Set 01 (Foundation Level) English Medium 100% Free Practice Test

West Bengal Board (WBBSE) Class 10 (Madhyamik) Mathematics: Compound Interest and Uniform Rate of Increase or Decrease Online Test (Set 01 (Foundation Level))

Compound Interest and Uniform Rate of Increase or Decrease — Set 01 (Foundation Level)

Practise free online CBT mock test for West Bengal Board (WBBSE) Class 10 (Madhyamik) Mathematics Chapter 6 'Compound Interest and Uniform Rate of Increase or Decrease'. 20 MCQs, 20-minute timer, instant scorecard, and step-by-step solutions aligned with official board syllabus.

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20 Mins

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20 Marks

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Instant Scorecard Step-by-Step Solutions WBBSE Madhyamik Blueprint

Chapter Study Guide & In-Depth Notes

Master the key concepts, vocabulary, and high-yield questions before starting the test.

3 Sections

WBBSE Class 10 Mathematics: Simple Interest (Chapter 2)

WBBSE Madhyamik Ganit Prakash Ch 2

In the WBBSE Class 10 Madhyamik Mathematics curriculum (Ganit Prakash / গণিত প্রকাশ), Simple Interest (Chapter 2) forms the cornerstone of practical commercial arithmetic (ব্যাবহারिक পাটিগণিত). In commercial finance, when capital is borrowed or deposited for a stipulated duration, the consideration fee paid for utilizing that capital is defined as Interest ($I$).

When interest is computed strictly and uniformly on the original principal sum ($P$) throughout the entire loan tenure—without compounding or adding accrued interest to the principal—it is termed Simple Interest. The fundamental mathematical equation governing simple interest is: $$I = \frac{P \times R \times T}{100}$$ Where $P$ = Principal amount (initial capital in ₹), $R$ = Annual rate of simple interest (expressed in percent per annum, $\%$ p.a.), $T$ = Time duration (which must strictly be measured in years), and $I$ = Total simple interest accrued.

Upon maturity, the aggregate sum of the initial principal and accrued interest is known as the Total Amount or Subriddhimul (মুলধন + সুদ / মিশ্রधन - $A$): $$A = P + I = P\left(1 + \frac{RT}{100}\right)$$ Under WBBSE examination conventions, whenever time is given in days (such as 73 days, 146 days, 219 days), it must be standardized to years by setting $T = \frac{\text{days}}{365}$ years. Similarly, monthly durations are converted using $T = \frac{\text{months}}{12}$ years. Mastering these formulas guarantees 100% accuracy in secondary board examination problems.

Core Moral & Key Takeaway:

Mastering the fundamental relationships $I = \frac{PRT}{100}$ and Amount $A = P(1 + \frac{RT}{100})$ guarantees full marks in WBBSE Madhyamik commercial arithmetic.

Core Formulas, Conversion Rules & Commercial Terminology

Formula Sheet & Key Concepts

Term / Formula	Type	Definition / Meaning	Explanation / Notes	Example / Usage
Simple Interest Formula	Master Formula	I = (P · R · T) / 100	Interest = (Principal × Rate × Time) / 100.	"Interest on ₹1000 at 5% for 2 years: (1000 × 5 × 2)/100 = ₹100."
Principal (P)	Derived Formula	P = (100 · I) / (R · T)	Initial capital borrowed or invested.	"If I=₹120, R=6%, T=2 yrs, then P = (100×120)/(6×2) = ₹1000."
Annual Rate (R)	Derived Formula	R = (100 · I) / (P · T) %	Annual percentage rate of interest.	"If P=₹500, T=3 yrs, I=₹60, then R = (100×60)/(500×3) = 4% p.a."
Time Duration (T)	Derived Formula	T = (100 · I) / (P · R) years	Duration of loan or investment in years.	"If P=₹800, R=5%, I=₹160, then T = (100×160)/(800×5) = 4 years."
Total Amount / Subriddhimul (A)	Identity	A = P + I = P(1 + RT/100)	Aggregate sum of principal and interest.	"Principal ₹2000 + Interest ₹300 = Total Amount ₹2300."
Days to Years Conversion	Rule	T = days / 365 years	73 days = 1/5 yr; 146 days = 2/5 yr; 219 days = 3/5 yr.	"Always convert 73 days into 1/5 year before computing interest."
Double Money Rule (A = 2P)	Shortcut	R · T = 100	When money doubles, I = P => R × T = 100.	"At 8% p.a., money doubles in 100/8 = 12.5 years."
Triple Money Rule (A = 3P)	Shortcut	R · T = 200	When money triples, I = 2P => R × T = 200.	"To triple money in 10 years, required rate is 200/10 = 20% p.a."

Key Features & Devices Explored:

Standard Unit Rule for Time

Always convert months into years (divide by 12) and days into years (divide by 365).

Dual Investment Modeling

Split total capital into x and (Total - x) to solve two-bank interest equations.

Subriddhimul Difference Method

The difference between amounts for two different durations yields the interest for that intervening period directly.

Effective Average Rate Method

Compute overall blended rate when multiple loans or investments are combined.

High-Yield Revision Points & Solved Madhyamik Board Exam Q&A

WBBSE Exam Revision Notes

⚡ High-Yield Exam Takeaways:

Time Unit Standardization: Time $T$ must always be in years. For daily periods, set $T = \frac{\text{days}}{365}$.
Constant Principal: In simple interest, the principal remains invariant each year, resulting in equal interest per annum.
Amount Difference Principle: If amount after 3 years is ₹600 and after 5 years is ₹700, then 2 years' interest is simply $700 - 600 = ₹100$.
Doubling / Tripling Shortcuts: For money to become $n$-fold, interest accrued is $I = (n - 1)P$, yielding $R \times T = (n - 1) \times 100$.
Term Distinction: Always check whether problem conditions specify Simple Interest or Compound Interest before applying formulas.

Frequently Asked Questions & Model Answers:

Q1 Find the simple interest on ₹2,000 at 6% per annum for 73 days.

Answer: Here, Principal $P = ₹2000$, Rate $R = 6\%$, and Time $T = \frac{73}{365} = \frac{1}{5}$ year. Using the simple interest formula: $$I = \frac{P \times R \times T}{100} = \frac{2000 \times 6 \times \frac{1}{5}}{100} = \frac{400 \times 6}{100} = ₹24$$ Thus, the required interest is ₹24.

Q2 In how many years will a sum of money double itself at 8% simple interest per annum?

Answer: Let the principal be $P$. When the sum doubles, Amount $A = 2P \implies$ Interest $I = 2P - P = P$. Using the time formula: $$T = \frac{100 \times I}{P \times R} = \frac{100 \times P}{P \times 8} = \frac{100}{8} = 12.5\text{ years}$$ Hence, the sum doubles in 12 years and 6 months.

Q3 At what annual rate of simple interest will the amount of a principal in 10 years become 7/5 times the principal?

Answer: Let the principal be $P$. Amount $A = \frac{7}{5}P \implies$ Interest $I = A - P = \frac{7}{5}P - P = \frac{2}{5}P$. Time $T = 10$ years. Using the rate formula: $$R = \frac{100 \times I}{P \times T} = \frac{100 \times \frac{2}{5}P}{P \times 10} = \frac{40P}{10P} = 4\%$$ Thus, the required rate is 4% per annum.

Q4 A person deposited ₹50,000 in two banks at 5% and 6% per annum simple interest. After 2 years, total interest earned was ₹5,400. Find the amount deposited in each bank.

Answer: Let the deposit in the first bank be $x$ and in the second bank be $(50000 - x)$. Total interest earned in 2 years is: $$\frac{x \times 5 \times 2}{100} + \frac{(50000 - x) \times 6 \times 2}{100} = 5400$$ $$10x + 12(50000 - x) = 540000 \implies 10x + 600000 - 12x = 540000$$ $$-2x = -60000 \implies x = ₹30,000$$ Thus, ₹30,000 was deposited in the first bank and $50000 - 30000 = ₹20,000$ in the second bank.

Sample Questions Preview

Free Sneak Peek

Here is a sneak peek of the questions included in this test set. Test your preparation by viewing the answer and detailed explanation before starting the timed exam.

What is the formula for Amount (A) at compound interest compounded annually?

বার্ষিক চক্রবৃদ্ধি সুদের পরিমাণ (A) এর সূত্র কি?

वार्षिक चक्रवृद्धि ब्याज पर राशि (ए) का सूत्र क्या है?

$A = P + (P * r * n)/100$

$A = P(1 + r/100)^n$ए = पी(1 + आर/100)^n

$A = P(1 - r/100)^n$ए = पी(1 - आर/100)^n

$A = P(1 + (rt)/100)$

Correct Answer: Option B

Explanation:

$A = P(1 + r/100)^n where P is principal, r is annual rate, and n is number of years.$

$A = P(1 + r/100)^n যেখানে P প্রধান, r হল বার্ষিক হার, এবং n হল বছরের সংখ্যা।$

ए = पी(1 + आर/100)^n जहां पी मूलधन है, आर वार्षिक दर है, और एन वर्षों की संख्या है।

Calculate the compound interest on Rs. 1,000 for 2 years at 10% per annum compounded annually.

টাকার উপর চক্রবৃদ্ধি সুদ গণনা করুন। বার্ষিক চক্রবৃদ্ধি বার্ষিক 10% হারে 2 বছরের জন্য 1,000।

रुपये पर चक्रवृद्धि ब्याज की गणना करें। 1,000 पर 2 साल के लिए 10% प्रति वर्ष की दर से वार्षिक चक्रवृद्धि दर दी जाएगी।

Rs. 220

Rs. 200

Rs. 210

Rs. 205

Correct Answer: Option C

Explanation:

$A = 1000(1.1)^2 = 1210. CI = 1210 - 1000 = Rs. 210.$

$A = 1000(1.1)^2 = 1210। CI = 1210 - 1000 = টাকা। 210।$

ए = 1000(1.1)^2 = 1210. सीआई = 1210 - 1000 = रु. 210.

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समय प्रबंधन एवं गति नियंत्रण

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सटीकता और नकारात्मक अंकन से सुरक्षा

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Syllabus Concepts Evaluated in this Chapter

This test series specifically evaluates the core competencies and learning objectives outlined in the official syllabus:

Foundational concepts of Principal ($P$), Annual Rate ($R$), Time ($T$), and Simple Interest ($I$).
Direct application of master formula $I = \frac{P \times R \times T}{100}$ to compute missing parameters.
Computation of Total Amount / Subriddhimul ($A = P + I$) and practical banking applications.
Precision conversion of daily and monthly durations into standard fractional years.
Rapid determination of rate or time for $n$-fold capital growth conditions.
Mathematical modeling and solution of two-bank split-investment word problems.

Exam Rules & Test Taking Guidelines

Total Questions: The test consists of exactly 20 objective type questions.
Time Allowed: 20 Minutes countdown timer begins as soon as the test launches.
Marking Scheme: +1.0 mark is awarded for each correct answer.
Zero Penalty: There is 0.0 negative marking for incorrect or unattempted questions.
Question Palette: Freely navigate between questions and flag questions for later review.
Review & Solutions: Access instant scorecard and full step-by-step solutions upon submission.

Frequently Asked Questions (FAQs)

Yes! Foundation Practice Set 01 for every chapter in West Bengal Board (WBBSE) Class 10 (Madhyamik) Mathematics is 100% free to attempt. Students can test their preparation without any subscription or payment.

This test strictly follows the official West Bengal Board (WBBSE) syllabus and curriculum for Class 10 (Madhyamik), covering textbook concepts, formulas, and board-standard MCQs for Chapter 6.

This dedicated test page is conducted in English Medium. If you prefer taking the test in Bengali or Hindi, you can switch using the language switcher bar at the top or toggle languages during the exam.

The test comprises 20 MCQs to be completed in 20 minutes. Each question carries +1.0 mark for a correct response, and there is 0.0 negative marking for incorrect or unattempted questions.

Yes! Instantly after submitting your test, you receive a comprehensive digital scorecard with accuracy analysis, time breakdown, and step-by-step verified explanations for all 20 questions.

Compound Interest and Uniform Rate of Increase or Decrease (Set 01 (Foundation Level))

20 MCQs • 20 Mins • 100% Free Practice Test

West Bengal Board (WBBSE) Class 10 (Madhyamik) Mathematics: Compound Interest and Uniform Rate of Increase or Decrease Online Test (Set 01 (Foundation Level))

Chapter Study Guide & In-Depth Notes

WBBSE Class 10 Mathematics: Simple Interest (Chapter 2)