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**Q1. Savita has two options to buy a house:****(a) She can pay a lumpsum amount of â‚¹ 22,00,000****Or****(b) She can pay â‚¹ 4,00,000 cash and balance in 18 annual instalments of â‚¹ 1,00,000 plus 10% interest on the unpaid amount.**

(b) Cash payment = â‚¹ 4,00,000

Balance = â‚¹ 22,00,000 â€“ â‚¹ 4,00,000 = â‚¹ 18,00,000

1st instalment = â‚¹ [1,00,000 + 10% of balance]

= â‚¹ [1,00,000 + 1,80,000] = â‚¹ 2,80,000

Balance after 1st instalment = â‚¹ [18,00,000 â€“ 1,00,000] = â‚¹ 17,00,000

2nd instalment = â‚¹ [1,00,000 + 10% of 17,00,000]

= â‚¹ [1,00,000 + 1,70,000] = â‚¹ [2,70,000]

Balance after 2nd instalment = â‚¹ 17,00,000 â€“ â‚¹ 1,00,000 = â‚¹ 16,00,000

âˆµ 3rd instalment = â‚¹ [1,00,000 + 10% of 16,00,000]

= â‚¹ [1,00,000 + 1,60,000] = â‚¹ 2,60,000

... and so on.

âˆµ Total amount in instalments = â‚¹ 2,80,000 + â‚¹ 2,70,000 + â‚¹ 2,60,000 + ..... to 18 terms

where a = 2,80,000, d = â€“ 10,000, n = 18

= â‚¹ 9 [560,000+17(-10,000)

= â‚¹ 9 [560,000 - 170,000]

= â‚¹ 9 = [390,000] = â‚¹ 35,10,000

âˆ´ Total cost of house = â‚¹ 35,10,000 + 4,00,000 = â‚¹ 39,10,000

Difference in costs of the house in two options

= â‚¹ 39,10,000 â€“ â‚¹ 22,00,000 = â‚¹ 17,10,000

âˆ´ (i) Amount donated towards Prime Minister Relief Fund = 50% of â‚¹ 17,10,000

(ii) Arithmetic Progressions

(iii) National Loyality

Each class has 2 sections.

âˆ´ Number of plants planted by class I = 1 x 2 = 2

Number of plants planted by class II = 2 x 2 = 4

Number of plants planted by class III = 3 x 2 = 6

Number of plants planted by class IV = 4 x 2 = 8

......................................................................................................

......................................................................................................

Number of plants planted by class XII = 12 x 2 = 24

The numbers 2, 4, 6, 8, ........................ 24 forms an A.P.

Here, a = 2, d = 4 â€“ 2 = 2

âˆµ Number of classes = 12

âˆ´ Number of terms (n) = 12

Now, the sum of n terms of the above A.P., is given by S

âˆ´ S

= 6 [4 + (11 x 2)]

= 6 x 26 = 156

Thus, the total number of trees planted = 156

Value shown: To enrich polution free environment.

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