Kanika was given her pocket money on Jan 1st, 2008. She puts Re 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?
NCERT Class X
Mathematics - Exemplar Problems
Chapter _ARITHMETIC PROGRESSIONS
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Answered by
340
Hi,
Kanika puts the money Rs 1 , Rs 2 , ..
Upto January moth ending .
Total amount from day 1 to 31st is
1+ 2 + 3 + .... + 31
a = 1 , common difference = d = 1
Sn = n /2 [ 2a + (n- 1 ) d ]
S31 = 31 /2 [ 2 × 1 + ( 31 - 1 ) 1 ]
= 31 /2 [ 2 + 30 ]
= ( 31 × 32 ) / 2
= 31 × 16
S31 = 496 ---( 1 )
She spent money = Rs 204-----( 2 )
Money she had = Rs 100 ---------( 3 )
Therefore ,
Kanika pocket money = ( 1 ) + ( 2 ) + ( 3 )
= 496 + 204 + 100
= Rs 800
I hope this helps you.
:)
Kanika puts the money Rs 1 , Rs 2 , ..
Upto January moth ending .
Total amount from day 1 to 31st is
1+ 2 + 3 + .... + 31
a = 1 , common difference = d = 1
Sn = n /2 [ 2a + (n- 1 ) d ]
S31 = 31 /2 [ 2 × 1 + ( 31 - 1 ) 1 ]
= 31 /2 [ 2 + 30 ]
= ( 31 × 32 ) / 2
= 31 × 16
S31 = 496 ---( 1 )
She spent money = Rs 204-----( 2 )
Money she had = Rs 100 ---------( 3 )
Therefore ,
Kanika pocket money = ( 1 ) + ( 2 ) + ( 3 )
= 496 + 204 + 100
= Rs 800
I hope this helps you.
:)
Answered by
18
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