please answer these questions
Answers
Answer:
i) (1)
ii)(2)
iii)(3)
iv)(1)
Step-by-step explanation:
Solution :-
Total amount repaid by Saurabh = Rs. 590000
The starting ins.talment = Rs. 5000
Amount is increased in every month in the ins.talment = Rs. 500
This situation is related to Arithmetic Progression.
We have ,
First term (a) = Rs. 5000
Common difference (d) = Rs. 500
The second ins.talment = 5000+500 =Rs. 5500
The AP: 5000,5500,6000,...,590000
We know that
nth term of an AP = an = a+(n-1)d.
i)The amount is paid by him in 20th ins.talment
= 20th term of the AP
=> a 20 = a+(20-1)d
=> a 20 = a+19d
=> a 20 = 5000+(19×500)
=> a 20 = 5000+9500
=> a 20 = 14500
The 20th ins.talment = Rs. 14,500
ii)The amount paid by him till 20th ins.talment
= Sum of all ins.talments from 1 to 20
We know that
Sum of first n terms = Sn= (n/2)[2a+(n-1)d]
We have , a = 5000, d = 500 and n = 20
=> S 20 = (20/2)[2(5000)+(20-1)(500)]
=> S 20 = (10)[10000+19×500)]
=> S 20 = 10(10000+9500)
=> S 20 = 10×19500
=> S 20 = 1,95,000
The amount paid by him till 20th inst.alment
= Rs. 1,95,000
iii)The amount paid by him till 30th ins.talment
= Sum of all ins.talments from 1 to 30
We know that
Sum of first n terms = Sn= (n/2)[2a+(n-1)d]
We have , a = 5000, d = 500 and n = 30
=> S 30 = (30/2)[2(5000)+(30-1)(500)]
=> S 30 = (15)[10000+29×500)]
=> S 30 = 15(10000+14500)
=> S 30 = 15×24500
=> S 30 =3,67,500
The amount paid by him till 30th ins.talment
= Rs. 3,67,500
iv) The amount still have to pay by him after 30th ins.talment =
Total Amount to be paid - The amount paid till 30th ins.talment
= 590000 - 367500
= Rs. 222500
Answer :-
i)The amount is paid by him in 20th ins.talment Rs. 14,500
ii)The amount paid by him till 20th ins.talment
= Rs. 1,95,000
iii)The amount paid by him till 30th ins.talment
= Rs. 3,67,500
iv)The amount still have to pay by him after 30th inst alment =Rs. 222500
Used formulae:-
- nth term of an AP = an = a+(n-1)d.
- Sum of first n terms = Sn= (n/2)[2a+(n-1)d]
- a = First term
- d = Common difference
- n = Number of terms