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

t_n = 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