Advertisements
Advertisements
Question
A merchant borrows ₹ 1000 and agrees to repay its interest ₹ 140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 10. Find the amount of the first instalment
Advertisements
Solution
The installments are in A.P.
Amount repaid in 12 instalments (S12)
= Amount borrowed + total interest
= 1000 + 140
∴ S12 = 1140
Number of instalments (n) = 12
Each instalment is less than the preceding one by ₹ 10.
∴ d = – 10
Now, Sn = `"n"/2 [2"a" + ("n" - 1)"d"]`
∴ S12 = `12/2 [2"a" + (12 - 1)(- 10)]`
∴ 1140 = 6[2a + 11(– 10)]
∴ 1140 = 6(2a – 110)
∴ `1140/6` = 2a – 110
∴ 190 = 2a – 110
∴ 2a = 300
∴ a = `300/2` = 150
∴ The amount of first instalment is ₹ 150.
RELATED QUESTIONS
The houses in a row numbered consecutively from 1 to 49. Show that there exists a value of x such that sum of numbers of houses preceding the house numbered x is equal to sum of the numbers of houses following x.
Find the sum of the following APs:
2, 7, 12, ..., to 10 terms.
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Find the sum of the following arithmetic progressions:
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum of all natural numbers between 1 and 100, which are divisible by 3.
Find the three numbers in AP whose sum is 15 and product is 80.
Find the sum of the first n natural numbers.
How many terms of the AP 63, 60, 57, 54, ….. must be taken so that their sum is 693? Explain the double answer.
In an A.P. the 10th term is 46 sum of the 5th and 7th term is 52. Find the A.P.
Divide 207 in three parts, such that all parts are in A.P. and product of two smaller parts will be 4623.
Rs 1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. For this complete the following activity.
Find the sum: 1 + 3 + 5 + 7 + ... + 199 .
Q.13
How many terms of the A.P. 27, 24, 21, …, should be taken so that their sum is zero?
The sum of the first 2n terms of the AP: 2, 5, 8, …. is equal to sum of the first n terms of the AP: 57, 59, 61, … then n is equal to ______.
The sum of first n terms of the series a, 3a, 5a, …….. is ______.
The sum of all two digit odd numbers is ______.
Kanika was given her pocket money on Jan 1st, 2008. She puts Rs 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?
In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021-22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year. |
Based on the above information answer the following questions.
- Find the production in the 1st year
- Find the production in the 12th year.
- Find the total production in first 10 years.
[OR]
In how many years will the total production reach 31200 cars?
The sum of A.P. 4, 7, 10, 13, ........ upto 20 terms is ______.
