Page 108 - Maths Skills - 8

106 Maths

According to the given condition,
300 – 2 (x + 22) – 2 x = 20

⇒ 300 – 2x – 44 – 2x = 20
⇒ 300 – 4x – 44 = 20
⇒ – 4x = 20 + 44 – 300
⇒ – 4x = – 236

⇒ 4x = 236
Hence, the speed of the first train = (x + 22) km/h

⇒ x = 236 = 59 = (59 + 22) km/h = 81 km/h, and the speed of the
second train = x = 59 km/h.
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x = 59 km/h

Exercise 7.2

1. Find three consecutive even numbers whose sum is 66.
2. Find three consecutive odd numbers whose sum is 69.

3. 2 of a number is 8 less than 2 of the number. Find the number.
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4. If 15 is added to four times a certain number, then the result obtained is 5 less from 6 times of that
number. Find the number.

5. The sum of the digits of a two-digit number is 9. The new number obtained by interchanging the digits
exceeds the given number by 27. Find the given number.

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6. If of a number is 16 less than the original number, then find the number.

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7. The sum of the two positive integers is 18. If the ratio of the integers is 5 : 4, then find the integers.
8. The sum of three consecutive multiples of 9 is 999. Find the multiples.
9. The sum of three consecutive multiples of 7 is 777. Find the multiples.

10. The denominator of a fraction is 4 more than the numerator. If the sum of the numerator and the
denominator is 20, then find the fraction.
11. Divide 300 into three parts such that the second part is half of the first part and the third part is 3 times
of the second part. Find the three different parts.
12. A is 10 years older than B and B is 15 years younger than C. If the sum of their ages is equal to their
father’s age, who is 40 years old, find the ages of A, B and C.

13. The difference of ages between two sisters is 10 years. 15 years ago if the elder one was twice as old as
the younger one, find their present ages.

14. One of the angles of a triangle is equal to the sum of the other two angles. If the ratio of the other two
angles is 1 : 2, find the angles of the triangle.
15. The perimeter of a rectangle is 240 m. If its length is decreased by 10% and breadth is increased by
20%, we get the same perimeter. Find the length and the breadth of the both the rectangles.

16. The length of a room is three and half times its width. If the perimeter of the floor of the room is 90 m,
find the length and width of the room.