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 instalment are paid he dies leaving one third of the dept unpaid find the value of the first instalment

Answer 1

______________________________

GIVEN :

=> A MAN BORROWED RS 3,600 IN 40 INSTALLMENTS

______________________________

=> THE GIVEN INSTALLMENTS ARE IN AP

______________________________

CONCEPTS FOR KNOWING :

=> t 1 = a = 1st INSTALLMENT

=> t 2 = 2nd INSTALLMENT

=> d = COMMON DIFFERENCE BETWEEN TWO CONSECUTIVE TERMS

=> n = NO. OF TERM

=> S = SUM

=> Sn = SUM OF n TERMS

_______________________________

FROM THE INFO ,

=> SUM OF TOTAL INSTALLMENTS :

=> S40 = 3,600

______________________________

STEP 1 :

=> TO USE THE FORMULA OF SUM OF TERMS IN THE GIVEN SITUATION :

______________________________

Sn = n / 2 * { 2a + d ( n - 1 ) }

=> S40 = 40 / 2 * { 2a + d ( 40 - 1 ) }

=> 3,600 = 20 * ( 2a + 39 d )

=> 3,600 = 20 * 2a + 780 d

=> DIVIDE BY 20

=> 180 = 2a + 39 d .................... 1

______________________________

STEP 2 :

=> TO FIND THE SUM HE PAID IN 30 INSTALLMENTS

______________________________

=> WHEN HE PAID FIRST 30 INSTALLMENTS HE DIED

=> HE HAS TO PAY REMAINING SUM WHICH IS 1/3RD OF TOTAL SUM

______________________________

1/3 rd OF TOTAL SUM

=> 1 / 3 * 3,600

=> 1,200 RS

______________________________

IN 30 INSTALLMENTS HE PAID RS

=> TOTAL SUM - REMAINING SUM

=> 3,600 - 1,200

=> 2,400

______________________________

STEP 3 :

=> TO USE THE FORMULA OF SUM OF 30 TERMS TO OBTAIN THE EQUATION

______________________________

S 30 = 2,400

=> S 30 = 30 / 2 { 2a + d ( 30 - 1 ) }

=> 2,400 = 15 * ( 2a + 29d )

=> 2,400 = 15 * 2a + 435d

=> DIVIDE BY 15

=> 160 = 2a + 29d ..................... 2

______________________________

STEP 4 :

=> SUBSTRACT EQN 2 FROM 1 TO GET THE VALUE OF d

_______________________________

180 = 2a + 39 d
-
160 = 2a + 29 d
____________

=> 20 = 10d

______________________________

=> d = 20 / 10

=> d = 2

______________________________

STEP 5 :

=> USE d TO FIND t 1

______________________________

PUT d = 2 IN EQUATION 1

=> 180 = 2a + 39 d

=> 180 = 2a + 39 * 2

=> 180 = 2a + 78

=> 2a = 180 - 78

=> 2a = 102

=> a = 102 / 2

=> a = 51 RS

_______________________________

FIRST INSTALLMENT :

=> t 1

=> 51 RS

______________________________

HOPE IT WILL HELP U ....

THANKS.....

______________________________

Answer 2

Answer:here is the answer

Step-by-step explanation: answer a=51