Page 122 - Start Up Mathematics_7

(b) Let the width of the rectangle be x.
∴ Length of the rectangle = (3x – 4) cm
Increased length = (3x – 4) + 7 = (3x + 3) cm
Decreased width = (x – 2) cm
2(Length + Width) = Perimeter
⇒ 2{(3x + 3) + (x – 2)} = 90
⇒ 2{4x + 1} = 90
90
⇒ 4x + 1 = 2
⇒ 4x + 1 = 45
⇒ 4x = 44
⇒ x = 11
Hence, width = 11 cm; length = 3x – 4 = 29 cm

EXERCISE 7.4

1. Six added to thrice of a number gives 33. Find the number.
2. If 19 is subtracted from a number, we get 11. Find the number.

3. The sum of three consecutive numbers is 69. Find the numbers.
4. The sum of two consecutive multiples of 5 is 65. Find the numbers.
5. Thrice a number, when increased by 7 gives 40. Find the number.
6. A number when added to its one-third equals 52. Find the number.
7. A number when multiplied by 3, exceeds itself by 40. Find the number.
8. A number is as much greater than 9 as it is less than 59. Find the number.
[Hint: (x – 9) = (59 – x)]
9. One-third of a number is smaller than its two-third by 7. Find the number.
10. Radha is 19 years younger than her cousin. After 5 years, their ages will be in the ratio
2 : 3. Find their present ages.
11. The sum of the ages of Subbu and Tobu is 18 years and the difference between their ages is
4 years. Find the ages of Subbu and Tobu.
12. The length of a rectangle is 6 cm more than its breadth. If the perimeter of the rectangle is
60 cm, find its length and breadth. Also find its area.
13. There are some 50 p coins and ` 1 coins in a bag. If the coins are equal in number and total
amount in the bag is ` 300, then find the number of 50 p and ` 1 coins in the bag.

An Age Old Trick
Guess your
A teacher instructed the class as follows: age!
• Think of your age
• Add 5 to it
• Multiply the result by 3
• Subtract 12
• Finally, divide it by 3 and tell me the answer
Your age is 1 less than the final answer you give.

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