CBSE Class 12-science Answered
Student put Rs.2 on first july, Rs.4 on 2-nd july , Rs.6 on 3-rd july and continue like this till end of july.
Hence , all the calculations are to be done by considering arithmetic progression with first term a = Rs.2 and
common difference d = Rs.2 .
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Part (i)
Total amount S saved at the end of July month is calculated as
S = (n/2) [ 2a + (n-1) d ]
in above relation, n = 31 day
S = (31/2) [ 4 + ( 30 × 2 ) ] = 31 × 32 = Rs. 992
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Part (ii)
He has spent Rs. 540 from his pocket money .
His total pocket money is sum of savings of month and expenditure.
Hos total pocket money = Rs. 992 + Rs. 540 = Rs. 1532
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Part (iii)
Amount put on last day of month is calculated as last term of aritmetic progression
tn = a + ( n-1) d
= 2 + ( 30) × 2 = Rs.62
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Part (iv)
Difference kept on 7-th day and 17-th day of this month is
S7 = (7/2) [ 2 × 2 + 6 × 2 ] = Rs. 56
S17 = ( 17/2 ) [ 2 × 2 + 16 × 2 ] = Rs. 306
Difference = S17 - S7 = Rs. (306 - 56 ) = Rs. 250
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Part (v)
Difference of money collected in first 10 days of the month and last 10 days of the month .
S10 = (10/2) [ 2 × 2 + 9 × 2 ] = Rs. 110
Last 10 days of month means from day 22 to day 31
Money put on day 22
t = 2 + (22-1) 2 = Rs. 44
Money collected in last 10 days of month is
S = (10/2) [ 2 × 44 + 9 × 2 ] = Rs. 530
Difference of money collected in first 10 days of the month and last 10 days of the month = Rs. (530 - 110 ) = Rs. 420
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part ( vi )
Money collected from first day to 11-th day
S11 = ( 11 / 2 ) [ 2 × 2 + ( 11 - 1 ) × 2 ] = Rs. 132
Money collected from first day to day 21
S21 = ( 21 / 2 ) [ 2 × 2 + ( 21 - 1 ) × 2 ] = Rs. 462
Money collected from day 11 to day 21 is = Rs. ( 462 -132) = Rs. 330
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If money put everyday is doubled , Then toal money collected at end of month is also doubled .
If money put everyday is doubled , then toal money= Rs. 992 × 2 = Rs.1984