What annual payment will discharge a debt of Rs. 580 due in 5 years, the rate being 8 % per annum.

M4maths Previous Puzzles

24 Oct 2014 Simple Interest

What annual payment will discharge a debt of Rs. 580 due in 5 years, the rate being 8 % per annum.

OPtion

1) 166.40
2) 126.5
3) 65.60
4) 150
5) 160
6) 120
7) 101.9
8) 100
9) 110
10) None of these

Solution

Let the annual payment be Rs. x
Then
(Amt of x for 4 years) + (Amt of x for 3 years) + (Amt of x for 2 years) + (Amt of x for 1 year) + x = 580
[x+ (x*4*8)/100] + [x+ (x*3*8)/100] + [x+ (x*2*8)/100] + [x+ (x*1*8)/100] + x = 580

5x + [(32x + 24x + 16x + 8x)/100] = 580
Solve
x = 100
Option 8)

Correct Option: 8 Best Solution (21)

RAKESH   10 years AGO

5x + x*8/100 *(1+2+3+4) = 580
=> 5.8x = 580
=> x = 100

Like? Yes (47) | No (16)  

Amit Kumar Pal   10 years AGO

The annual payment that will discharge a debt of rs A due in "t" years at the rate of interest r% per annum is

(100A)/(100t+((rt(t-1))/2))

here A=580
t=5
r=8

hence (100*580)/(100*5+((8*5(5-1))/2))
=100 (answer)

Like? Yes (28) | No (7)  

Kushagra Tiwari   10 years AGO

let the annul installment be x then
{x+(x*4*8/100)} + {x+(x*3*8/100)} + {x+(x*2*8/100)} + {x+(x*1*8/100)} +x = 580

on solving it is 33x/25 + 31x/25 + 29x/25 + 27x/25 =580
(120+25)x = 580*25
on solving x= 100

Like? Yes (38) | No (25)  

Raj   10 years AGO

let the annual instalment be x.
[x+(x*4*8)/100]+[x+(x*3*8)/100]+[x+(x*2*8)/100]+[x+(x*1*8)/100]+x=580
(120+25)x=580*25
x=100

Like? Yes (4) | No   

Chandra chur anand   10 years AGO

let d amount be payment= x
so amount being paid 4th,3rd,2nd,1st yr are=
x+132x/100+124x/100+116x/100+108x/100=580x/100
so 580x/100=580
x=100 rs ans

Like? Yes (6) | No (4)  

NAVEEN KUMAR   10 years AGO

Let annual installment =Rs. x
then,
[x+(x*4*8/100)]+[x+(x*3*8/100)]+[x+(x*2*8/100)]+[x+(x*1*8/100)]+x=580
=>33x/25 + 31x/25 + 29x/25 + 27x/25 + x = 580
=>x=100
hence,annual installment =Rs.100(option 8 )

Like? Yes (17) | No (16)  

Abhishek Vishwakarma   10 years AGO

let the annul installment be x then
{x+(x*4*8/100)} + {x+(x*3*8/100)} + {x+(x*2*8/100)} + {x+(x*1*8/100)} +x = 580

on solving it is 33x/25 + 31x/25 + 29x/25 + 27x/25 =580
(120+25)x = 580*25
on solving x= 100

Like? Yes (2) | No (1)  

santosh kumar patel   10 years AGO

m=na+r*a/100*y*n(n-1)/2
m=580
n=5
y=1
r=8%
a=annual payment
580=5a+8a/100*5*4/2
29a=2900
a=100 ans.

Like? Yes (3) | No (2)  

Aman Narang   10 years AGO

Let annual payment =x;
then [x+(x*4*8/100)]+[x+(x*3*8/100]+[x+(x*2*8/100)]+[x+(x*1*8/100)]+x=580
33 x/25+31 x/25+29 x/25+27 x/25+x=580
(120+25)x=580*25
x=100

Like? Yes (2) | No (1)  

Priya Dharshini   10 years AGO

let the annual payment be $X;
so 580 dept means = SI + Principal amount
X +
(X+(X*8*1)/100)+
(X+(X*8*2)/100)+
(X+(X*8*3)/100)+
(X+(X*8*4)/100)=580;


X+(108X/100)+(116X/100)+(124X/100)+(132X/100)=580;


580X/100=580;
X=100;..................ANS

Like? Yes (3) | No (2)  

Anand   10 years AGO

580=x/(1+0.08)+x/(1+0.08)^2+x/(1+0.08)^3+x/(1+0.08)^4+x/(1+0.08)^5
x=100

Like? Yes (2) | No (2)  

Abhishek Porwal   10 years AGO

Amount of each installment =(100*P) / [(100*n)+{n(n-1)*r}/2]
where, n=time= 5 years
p=580,
r=8%
on Putting the values we will get
Amount = Rs. 100

Like? Yes (4) | No (4)  

BHASKAR MANDAL   10 years AGO

let the annual installment be x, then
[x+(x*4*8)/100] + [x+(x*3*8)/100] + [x+(x*2*8)/100] + [x+(x*1*8)/100] + x = 580

=> 33x/25 + 31x/25 + 29x/25 + 27x/25 + x = 580
=>(120+25) x = 580*25
=> 145 x = 14500
=> x = 100
option 8 is the answer

Like? Yes (3) | No (3)  

Shreya Tiwari   10 years AGO

let the annul installment be x then
{x+(x*4*8/100)} + {x+(x*3*8/100)} + {x+(x*2*8/100)} + {x+(x*1*8/100)} +x = 580

on solving it is 33x/25 + 31x/25 + 29x/25 + 27x/25 =580
(120+25)x = 580*25
on solving x= 100

Like? Yes (3) | No (3)  

Biswajit Saha   10 years AGO

let each payment be x
then
(x+(x*8*1)/100)+ ....... +(x+(x*8*4)/100) +x =580
x=100

Like? Yes (2) | No (2)  

Masood Ahmad   10 years AGO

X=100A/{100*t+rt (t-1)/2}
=100*580/{100*5+8*5(5-1)/2}
=100*580/580
=100

Like? Yes (2) | No (2)  

niraj   10 years AGO

5x+x*8*1/100=580
500x + 8x =58000

Like? Yes (7) | No (7)  

Subhash Kumar   10 years AGO

Ans : 100

Like? Yes (3) | No (4)  

Chirag Ranjan Lahiri   10 years AGO

Let the annual installment be Rs x.
Then, [x+(x*4*8/100)] + [x+(x*3*8/100)] + [x+(x*2*8/100)] + [x+(x*1*8/100)] + x = 580
On simplifying we get, (120 + 25)*x = 580 * 25
=> x = 100 (answer)

Like? Yes (2) | No (3)  

Sandeep Kumar   10 years AGO

100

Like? Yes (1) | No (3)  

Ravi Kumar   10 years AGO

option 8) 100

Like? Yes (2) | No (4)