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, `S_n = n/2 [2a + (n - 1)d]`
∴ `S_12 = 12/2 [2a + (12 - 1)(-10)]`
∴ 1140 = 6[2a + 11(– 10)]
∴ 1140 = 6(2a – 110)
∴ `1140/6` = 2a – 110
∴ 190 = 2a – 110
∴ 2a = 300
∴ a = `300/2`
∴ a = 150
∴ The amount of first instalment is ₹ 150.
RELATED QUESTIONS
Ramkali saved Rs 5 in the first week of a year and then increased her weekly saving by Rs 1.75. If in the nth week, her week, her weekly savings become Rs 20.75, find n.
Find the sum of the following arithmetic progressions:
`(x - y)/(x + y),(3x - 2y)/(x + y), (5x - 3y)/(x + y)`, .....to n terms
Find the sum of first 22 terms of an A.P. in which d = 22 and a = 149.
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?
How many three-digit numbers are divisible by 9?
Find the value of x for which (x + 2), 2x, (2x + 3) are three consecutive terms of an AP.
Choose the correct alternative answer for the following question .
In an A.P. first two terms are –3, 4 then 21st term is ...
The A.P. in which 4th term is –15 and 9th term is –30. Find the sum of the first 10 numbers.
The sum of first n terms of an A.P. is 5n − n2. Find the nth term of this A.P.
If 18, a, b, −3 are in A.P., the a + b =
Q.11
Q.17
Find the sum of first 20 terms of an A.P. whose first term is 3 and the last term is 57.
Find the sum of first 1000 positive integers.
Activity :- Let 1 + 2 + 3 + ........ + 1000
Using formula for the sum of first n terms of an A.P.,
Sn = `square`
S1000 = `square/2 (1 + 1000)`
= 500 × 1001
= `square`
Therefore, Sum of the first 1000 positive integer is `square`
Find the sum of numbers between 1 to 140, divisible by 4.
The first term of an AP of consecutive integers is p2 + 1. The sum of 2p + 1 terms of this AP is ______.
Find the sum of first seven numbers which are multiples of 2 as well as of 9.
Find the sum of first 'n' even natural numbers.
The sum of the 4th and 8th term of an A.P. is 24 and the sum of the 6th and 10th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.
