**Question 1 :**

A man repays a loan of 65,000 by paying 400 in the first month and then increasing the payment by 300 every month. How long will it take for him to clear the loan?

**Solution :**

For the first month he is paying = 400

payment of second month = 400 + 300 = 700

payment of 3rd month = 700 + 300 = 1000

400 + 700 + 1000, ................

loan amount = 65000

(n/2)[2a + (n - 1)d] = 65000

(n/2)[2(400) + (n - 1)300] = 65000

(n/2)[800 + 300n - 300] = 65000

(n/2)[500 + 300n] = 65000

(n/2)[5 + 3n] = 650

n[5 + 3n] = 1300

5n + 3n^{2} = 1300

3n^{2 }+ 5n - 1300 = 0

3n^{2} - 60n + 65n - 1300 = 0

3n(n - 20) + 65(n - 20) = 0

(n - 20) (3n + 65) = 0

n = 20 or n = -65/3 (not acceptable)

So, he will clear the loan amount in 20 months.

**Question 2 :**

A brick staircase has a total of 30 steps. The bottom step requires 100 bricks. Each successive step requires two bricks less than the previous step.

(i) How many bricks are required for the top most step?

(ii) How many bricks are required to build the stair case?

**Solution :**

Let "l" be the number of bricks in the last step

Number of bricks in the 1st step (a) = 100

Number of bricks in the 2nd step = 100 - 2 = 98

d = 98 - 100 = -2

number of steps (n) = 30

(i)

t_{30} = a + 29d

= 100 + 29(-2)

= 100 - 58

= 42

So, we will have 42 bricks in the top most step.

(ii) How many bricks are required to build the stair case?

S_{n} = (n/2)[a + l]

= (30/2)[100 + 42]

= 15(142)

= 2130

**Question 3 :**

If S_{1, }S_{2}, S_{3},....Sm are the sums of n terms of m A.P.’s whose first terms are 1,2, 3,...m and whose common differences are 1, 3, 5,..., (2m -1) respectively, then show that S_{1} + S_{2} + S_{3} +............S_{m} = (mn/2)(1 + mn)

**Solution :**

n = [(l-a)/d] + 1

n = [((2mn - n + 1) - (1 + n))/2n] + 1

n = [(2mn - n + 1 - 1 - n)/2n] + 1

n = [(2mn - 2n)/2n] + 1

n = (m - 1) + 1

n = m

S_{1} + S_{2} + S_{3} +............S_{m}

Hence proved.

**Question 4 :**

Find the sum

**Solution :**

a = (a-b)/(a+b)

d = (3a-2b)/(a+b) - (a-b)/(a+b)

d = [3a - 2b -(a - b)]/(a + b)

d = [3a - 2b -a + b]/(a + b)

d = (2a - b) / (a + b)

Sn = (n/2)[2a + (n - 1)d]

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**