# Shamshad Ali buys a scooter for $Rs22000.$ He pays $4000$ cash and agrees to pay the balance in annual instalment of $Rs1000$ plus $10% $ interest on the unpaid amount. How much will the scooter cost him?

Last updated date: 19th Mar 2023

•

Total views: 305.7k

•

Views today: 2.84k

Answer

Verified

305.7k+ views

Hint: In order to solve this type of question, first we have to calculate the remaining balance and then we have to calculate the interest on the unpaid amount. After that we have to calculate the number of instalments.

Complete step-by-step answer:

Given-

Cost of the scooter = $Rs22000$

Down payment made by cash = $Rs4000$

Remaining balance =$

Rs22000 - Rs4000 \\

= Rs18000 \\

$

Annual instalment $ = 1000 + $ Interest on unpaid amount $@10% $

${1^{st}}$ Instalment, unpaid amount $ = 18000$

Interest on unpaid amount $ = \dfrac{{10}}{{100}} \times 18000 = 1800$

Therefore, amount of instalment $ = 1000 + 1800 = 2800 - - - - \left( 1 \right)$

${2^{nd}}$ Instalment, unpaid amount$ = 18000 - 1000 = 17000$

Interest on unpaid amount $ = = \dfrac{{10}}{{100}} \times 17000 = 1700$

Therefore, amount of instalment $ = 1000 + 1700 = 2700 - - - - - \left( 2 \right)$

${3^{rd}}$ instalment, unpaid amount $ = 17000 - 1000 = 16000$

Interest on unpaid amount $ = = \dfrac{{10}}{{100}} \times 16000 = 1600$

Therefore, amount of instalment $ = 1000 + 1600 = 2600 - - - - - \left( 3 \right)$

Thus, from (1), (2) and (3) our instalments are $2800,2700,2600.$

Number of instalments $ = \dfrac{{\operatorname{Remaining} {\text{ }}balance{\text{ }}left}}{{balance{\text{ cleared per instalment}}}} = \dfrac{{18000}}{{1000}} = 18$

So, our instalments are $2800,2700,2600,......to{\text{ 18terms}}{\text{.}}$

We can observe that this is an $AP$ as difference between consecutive terms is an $AP.$

Hence,

First term $\left( a \right) = 2800$

Common difference= $\left( d \right) = 2700 - 2800 = - 100$

Number of terms$ = n = 18$

We need to calculate total amount paid in $18$ instalments i.e.$\left( {2800 + 2700 + 2600......to{\text{ 18terms}}} \right)$

We have to apply the formula

${S_n} = \dfrac{n}{2}\left( {2a + \left( {n - 1} \right)d} \right)$

Where,

$

{S_n} = sum{\text{ of n terms of A}}{\text{.P}}{\text{.}} \\

{\text{n = number of terms}}{\text{.}} \\

{\text{a = first term and d = common difference}} \\

$

Putting the value of $n = 18,a = 2800{\text{ }}and{\text{ d = - 100}}$

${S_n} = \dfrac{{18}}{2}\left( {2\left( {2800} \right) + \left( {18 - 1} \right)\left( { - 100} \right)} \right)$

Or ${S_n} = 9\left( {5600 + 17\left( { - 100} \right)} \right)$

Or ${S_n} = 9\left( {5600 - 1700} \right)$

Or ${S_n} = 9\left( {3900} \right)$

Or ${S_n} = 35100$

Hence, the amount paid in $18$ instalments$ = Rs{\text{ }}35100$

Note: Whenever we face these type of question the key concept is that we have to calculate the annual instalment with annual interest and then total number of instalment and simply substituting the value of $\left( a \right)$ and $\left( d \right)$ in the equation ${S_n} = \dfrac{n}{2}\left( {2a + \left( {n - 1} \right)d} \right)$ .

Complete step-by-step answer:

Given-

Cost of the scooter = $Rs22000$

Down payment made by cash = $Rs4000$

Remaining balance =$

Rs22000 - Rs4000 \\

= Rs18000 \\

$

Annual instalment $ = 1000 + $ Interest on unpaid amount $@10% $

${1^{st}}$ Instalment, unpaid amount $ = 18000$

Interest on unpaid amount $ = \dfrac{{10}}{{100}} \times 18000 = 1800$

Therefore, amount of instalment $ = 1000 + 1800 = 2800 - - - - \left( 1 \right)$

${2^{nd}}$ Instalment, unpaid amount$ = 18000 - 1000 = 17000$

Interest on unpaid amount $ = = \dfrac{{10}}{{100}} \times 17000 = 1700$

Therefore, amount of instalment $ = 1000 + 1700 = 2700 - - - - - \left( 2 \right)$

${3^{rd}}$ instalment, unpaid amount $ = 17000 - 1000 = 16000$

Interest on unpaid amount $ = = \dfrac{{10}}{{100}} \times 16000 = 1600$

Therefore, amount of instalment $ = 1000 + 1600 = 2600 - - - - - \left( 3 \right)$

Thus, from (1), (2) and (3) our instalments are $2800,2700,2600.$

Number of instalments $ = \dfrac{{\operatorname{Remaining} {\text{ }}balance{\text{ }}left}}{{balance{\text{ cleared per instalment}}}} = \dfrac{{18000}}{{1000}} = 18$

So, our instalments are $2800,2700,2600,......to{\text{ 18terms}}{\text{.}}$

We can observe that this is an $AP$ as difference between consecutive terms is an $AP.$

Hence,

First term $\left( a \right) = 2800$

Common difference= $\left( d \right) = 2700 - 2800 = - 100$

Number of terms$ = n = 18$

We need to calculate total amount paid in $18$ instalments i.e.$\left( {2800 + 2700 + 2600......to{\text{ 18terms}}} \right)$

We have to apply the formula

${S_n} = \dfrac{n}{2}\left( {2a + \left( {n - 1} \right)d} \right)$

Where,

$

{S_n} = sum{\text{ of n terms of A}}{\text{.P}}{\text{.}} \\

{\text{n = number of terms}}{\text{.}} \\

{\text{a = first term and d = common difference}} \\

$

Putting the value of $n = 18,a = 2800{\text{ }}and{\text{ d = - 100}}$

${S_n} = \dfrac{{18}}{2}\left( {2\left( {2800} \right) + \left( {18 - 1} \right)\left( { - 100} \right)} \right)$

Or ${S_n} = 9\left( {5600 + 17\left( { - 100} \right)} \right)$

Or ${S_n} = 9\left( {5600 - 1700} \right)$

Or ${S_n} = 9\left( {3900} \right)$

Or ${S_n} = 35100$

Hence, the amount paid in $18$ instalments$ = Rs{\text{ }}35100$

Note: Whenever we face these type of question the key concept is that we have to calculate the annual instalment with annual interest and then total number of instalment and simply substituting the value of $\left( a \right)$ and $\left( d \right)$ in the equation ${S_n} = \dfrac{n}{2}\left( {2a + \left( {n - 1} \right)d} \right)$ .

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE