Page 66 - SM inner class 8.cdr

Example 12: I have a total of ` 300 in coins of Solution: Since the ratio of the present ages of
de nom i na tion ` 1, ` 2 and ` 5. The num ber of ` Ram and Rahim is given as 4:3, let the present
2 coins is 3 times the num ber of ` 5 coins. The age of Ram be (4x ) years.
to tal num ber of coins is 160. How many coins Present age of Rahim will be 3x years.
of each de nom i na tion are with me?
After four years Ram’s age = (4x + ) years
4
Solution: Let ` 5 coin = x
4
Rahim’s age = (3x + ) years
` 2 coins = 3x According to the given condition
Total number of coins = 160 = (4x + ):(3x + ) = :5
4
6
4
So, ` 1 coin = 160 - (x + 3x) i.e. 4x + 4 = 6
= 160 - 4x 3x + 4 5
Total money = ` 300 By cross multiplication we get
(
(
=
5(x) + 2(3x) + 1(160 - 4x) = 300 5 4x + 4) = 6 3x + 4) or 20x + 20 18x + 24
5x + 6x + 160 - 4x = 300 or 20x - 18x = 24 - 20 (transposing 18x to LHS
11x - 4x + 160 = 300 and 20 to RHS)
7x + 160 = 300 or 2x = 4
7x = 300 - 160 x = 2
2
7x = 140 \ Present age of Ram = (4 ´ ) years i.e. 8 years
2
So, ` 5 coins = 20 Present age of Rahim = (3 ´ ) years i.e. 6 years
` 2 coins = 3x = 3(20)=60 Verification:
` 1 coins = 160 -(20 + 60) Present age of Ram 8 4
= =
` 1 coins = 80 Present age of Rahim 6 3
Example 13. The present ages of Ram and Which is same as given:
Rahim are in the ratio 4:3. Four years later, Hence, the solution is correct.
their ages will be in the ratio 6:5. What are
their present ages?

E xercise 8.2

1. A number is 12 more than the other. Find the numbers if their sum is 48.

2. Twice the number decreased by 22 is 48. Find the number.
3. Seven times the number is 36 less than 10 times the number. Find the number.
4 3
4. of a number is more than of the number by 5 . Find the number.
5 4
5. The sum of two consec u tive even numbers is 38. Find the numbers.
6. The sum of three consec u tive odd numbers is 51. Find the numbers.
7. The sum of two numbers is 85. If one number exceeds the other by 7, find the numbers.
8. The age of father is 20 years more than twice the age of the son. If sum of their ages is 65 years, find the
age of the son and the father.
9. The length of a rect an gle is twice its breadth. If perim e ter of rect an gle is 66 cm, find its length and
breadth.
10. Among the two supple men tary angles, the measure of the larger angle is 36° more than the measure of
smaller. Find their measures.
11. My mother is 12 years more than twice my age. After 8 years, my mother's age will be 20 years less
than three times my age. Find my age and my mother's age.

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Mathematics In Focus - 8