Question

(16) Sum of the digits of a two digit number is 7.When we interchange the digits,it is foundthat the resulting new number is greater than the original number by 45

(17) There is a narrow rectangular plot, reserved for a school. The length and breadth of the plot are in the ratio 2:3. At the rate Rs 50 per metre it will cost Rs 100000 to fence the plot.

What are the dimensions of the plot ?

(18) Ravina thinks of a number and subtracts 3/5 from it. She multiplies the result by 7.The

result now obtained is 5 times the same number she thought of .What is the number ?
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Answer 1

Answer:

Step-by-step explanation:

16) Let thedigits at tens place and ones place be x and 9 − xrespectively.

Therefore,original number = 10x + (9 − x) = 9x + 9

Oninterchanging the digits, the digits at ones place and tens placewill be x and 9 − x respectively.

Therefore,new number after interchanging the digits = 10(9 − x) +x

= 90 − 10x + x

= 90 − 9x

Accordingto the given question,

New number= Original number + 27

90 −9x = 9x + 9 + 27

90 −9x = 9x + 36

Transposing9x to R.H.S and 36 to L.H.S, we obtain

90 −36 = 18x

54 = 18x

Dividingboth sides by 18, we obtain

3 = xand 9 − x = 6

Hence, thedigits at tens place and ones place of the number are 3 and 6respectively.

Therefore,the two-digit number is 9x + 9 = 9 × 3 + 9 = 36

Answer 2

Answer:

(16) Let the ten's place be x and unit's place be y.

According to the question,

x + y = 7        ....(1)

Original number: x(10) + y(1) = 10x + y

Reversed number: y(10) + x(1) = 10y + x

According to the second part of the question,

Reversed number = Original number + 45

10y + x = 10x + y + 45

9y - 9x = 45

9[y - x] = 45

y - x = 5        ....(2)

Now if we solve the two equations (1) and (2), we would get,

y = 6 and x = 1

Therefore, the original number is = 1(10) + 6(1) = 10 + 6 = 16[answer]

(17) Given that the length and breadth of the rectangular plot are in the ratio 2:3. So let the length of the plot be 2x and breadth of the plot be 3x.

The perimeter of rectangle = 2(l + b)

The perimeter of the rectangular plot = 100000 / 50

= 2000 m

Therefore,

2(l + b) = 2000

2(2x + 3x) = 2000

2(5x) = 2000

10x = 2000

x = 200

So, the length of the plot is 2(200) = 400 m and the breadth is 3(200) = 600m.

(18) Let the number be x.

According to the question,

(x - 3/5)7 = 5x

7x - 21/5 = 5x

2x = 21/5

x  = 21/10

So, the number is 21/10.

Hope this helps you!!!