Question

Q1. Sum of the digits of a two digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?
Q2. There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11 : 4. At the rate of ₹ 100 per metre, it will cost the village panchayat ₹ 75000 to fence the plot. What are the dimensions of the plot?
Q3. Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him ₹ 50 per metre and trousers material that costs him ₹ 90 per metre. For every 3 metres of the shirt material, he buys 2 metres of the trouser material. He sells the materials at 12% and 10% profit respectively. His total sale is ₹ 36,600. How much trouser material did he buy?

Chapter :-
Linear Equation in one variable

Answer 1

Answer:

Answer (1)

Given :-

• Sum of two digit number is 9
• When the number interchange the number was 27 greater than other

To Find :-

The number

Solution :-

Let the number at unit place be x

The tens number will be 9 - x

Original number = x + 10(9- x)

Interchange number = 10x + (9-x)

Interchange number = Original number + 27

10x + (9 - x) = x + 10 (9 - x) + 27

10x + 9 – x = x + 90 – 10x + 27

10x - x + 9 = x- 10x + 117

9x + 9 = -9x + 117

9x + 9x = 117 - 9

18x = 108

x = 108/18

x = 6

Number at unit place is 6

Number at tens place is 9 - x = 3

$\huge \fbox{Number = 36}$

Answer (2)

Given :-

• Ratio of length: Breadth = 11:4
• Cost of fencing per metre = ₹100
• Total cost = ₹75,000

To Find :-

Dimensions of plot

Solution :-

When we fence a plot we find its perimeter.

Perimeter = Total cost/Cost of 1 metre

Perimeter = 75000/100

Perimeter = 750 m

Now,

As we know that

Perimeter of rectangle = 2(l + b)

Let the ratio be 11 x and 4x.

750 = 2(11x + 4x)

750 = 2(15x)

750 = 30x

x = 750/30

x = 25 m

Dimensions are :-

$\huge \fbox{Length = 275 m}$

$\huge \fbox{Breadth = 100 m }$

Answer (3)

Given :-

• Cost of shirt material = ₹50 per m
• Cost of trouser material = ₹90 per m
• For every 3 metres of the shirt material, he buys 2 metres of the trouser material. He sells the materials at 12% and 10% profit respectively. His total sale is ₹ 36,600

To Find :-

How much trouser material did he buy?

Solution :-

Let the shirt material bought be 3x and trouser material bought be 2x

Cost of shirt material = 50 × 3x = ₹ 150x

Cost of trouser material = 90 × 2x = ₹ 180x

For Shirt Material

(150x + 150x × 12/100)

(150x + 18x)

168x

For Trouser Material

(180x + 180x × 10/100)

(180x + 180x × 1/10)

(180x + 18x)

198x

According to Question

168x + 198x = 36,600

366x = 36,600

x = 36,600/366

x = 100

$\huge \fbox{Trouser Material = 200 M}$