Question

on a certain sum of money the diffrence between compound interets payable half yearly and the simple interest for a yrar is 180
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Answer 1

Given :

• on a certain sum of money the diffrence between compound interets payable half yearly and the simple interest for a yrar is 180

To find :

• the sum lent out if rate of interest in both the cases is 10%

Solution :

Let the principal be Rs x

$S.I. \: for \: 1 \: year \: at \: 10 \: percent \: per \: annum \\ \\ = \frac{x \times 10 \times 1}{100} \\ \\ = rs \frac{x}{10}$

$Rate \: of \: interest \: per \: conversion \: period \: (half-year) \\ \\ = \frac{1}{2} \: of \: 10 \: percent \\ \\ = 5 \: percent$

$and \: n(the \: number \: of \: conversion \: periods) = 2 \\ \\ CI = Rs \: x[(1 + \frac{5}{100})^{2} - 1] \\ \\ = Rs \: x( \frac{21}{20} \times \frac{21}{20} - 1) \\ \\ = Rs \: x = \frac{441}{400} - 1 \\ \\ = \frac{41}{400} x \\ \\ \therefore \: CI - SI = Rs \frac{41}{400} x - Rs \: \frac{x}{10} \\ \\ = Rs( \frac{41}{400} - \frac{1}{10})x \\ \\ = Rs \: \frac{x}{400} \\ \\ according \: to \: the \: given \: information \\ \\ = \frac{x}{400} = 180 \\ \\ x = 72000 \\ \\ \therefore \: the \: sum \: lent \: out = Rs \: 72000$

Answer 2

Answer:

Let the sum be ₹ P

• Principal = P
• Rate = 10% p.a
• Time = 1 year

CASE ❶ : To Find Compound Interest

• Rate = 10/2 = 5 % p.a

• Time = 1 × 2 = 2 year

→ Amount = P × (1 + R/100)ⁿ

→ Amount = P × (1 + 5/100)²

→ Amount = P × (105/100)²

→ Amount = P × (21/20)²

→ Amount = 441/400 P

Therefore,

→ Compound intrest = Amount - Principal

→ Compound intrest = 441/400 P - P/1

→ Compound intrest = 441 P - 400P/400

→ Compound intrest = 41P/400

________________...

CASE ❷ : To Find Simple Intrest

➝ Simple Intrest = P × 10 × 1/100

➝ Simple Intrest = P/10

▩ According to Question now :

➳ Compound Interest - Simple Intrest = 180

➳ 41 P/400 - P/10 = 180

➳ 41 P - 40 P/400 = 180

➳ P/400 = 180

➳ Principal = 180 × 400

➳ Principal = ₹ 7200

Therefore,

• Sum lent out = ₹ 7200

__________________....

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$\tt 1) Profit = SP - CP$

$\tt 2) Loss = CP - SP$

$\tt 3) Profit\% = (Profit \:in \:Rs.)*100/CP$

$\tt 4) Loss\% = (Loss \:in \:Rs.)*100/CP$

$\tt 5) SP = CP*(100+P\%)/100$

$\tt 6) SP = CP*(100-L\%)/100$

$\tt 7) CP = SP*100/(100+P\%)$

$\tt 8) CP = SP*100/(100-L\%)$

$\tt 9) Discount =MP - SP$

$\tt 10) Discount\%=(Discount \:in \:Rs.)*100/MP$

$\tt 11) MP = SP*100/(100-D\%)$