CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A man arranges to pay off a debt of Rs. 3600 by 40 annual installments which form an arithmetic series. When 30 of the installments are paid, he dies leaving one third of the debt unpaid, find the value of the first installment.

A
Rs. 53
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Rs. 54
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Rs. 50
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Rs. 51
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D Rs. 51
Let the first instalment = Rs. a
Common difference between installment = Rs. d.
Case 1:
A man pays of a debit of Rs. 3600 in 40 annual statements.
n=40,S40= Rs. 3600
Sn=n2[2a+(n1)d]
S40=402[2a+(401)d]
3600=20[2a+39d]
2a+39d=180 .....(1)
Case 2:
Man die leaving one third of installment unpaid.
Then unpaid amount = 13×3600=1200
Hence, debt paid in 30 installment =36001200=2400
Heren=30,s30=2400
Sn=n2[2a+(n1)d]
S30=302[2a+(301)d]
2400=15[2a+29d]
2a+29d=160 ........(2)
Subtracting equation (1) by equation (2),
10d=20
d=2
Putting the value of d in equation (1), we get
2a+39d=180
2a+39×2=180
2a=102
a=51
Hence, the first term paid by man = Rs. 51.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Solving Linear Equations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon