Page 148 - Start Up Mathematics_8 (Non CCE)

EXERCISE 8.4

1. The sum of two numbers is 70. Their difference is 16. Find the numbers.
2. The difference between two positive integers is 36. The quotient when one integer is divided by the
other is 4. Find the two integers.
3. Two numbers are such that the first number is 5 times the second number. If 10 is added to both the
numbers, the first number becomes 3 times the second number. Find the two numbers.
4. Divide 60 into two parts, such that 3 times the smaller part may exceed 100 by as much as
9 times the bigger falls short of 200.
5. A two-digit number is such that the sum of its digits is 8. If 54 is subtracted from the number, its
digits are reversed. Find the number.
6. The difference between the squares of two consecutive numbers is 31. Find the numbers.
7. The numerator of a fraction is 8 less than the denominator. If the numerator is increased by 17 and
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the denominator is decreased by 1, the new fraction obtained is . Find the fraction.
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8. The digit at the tens place of a two-digit number is 3 times the digit at the units place. If the digits
are reversed, the new number will be 36 less than the original number. Find the number.

9. Manav has a small box with ` 740 in coins of denominations ` 1, ` 2 and ` 5. If the number of coins of
denomination of ` 2 are 3 times the number of coins of denomination of ` 1 and the number of coins
of denomination of ` 5 are twice the number of coins of ` 2, how many coins of each denomination does
Manav has?
10. The organizers of a story writing competition decided that the winner in the competition will get a
prize of ` 200 and a participant who participates and does not win will get a prize of ` 50. The total
prize money distributed is ` 6,000. Find the number of winners, if the total number of participants is
60.
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11. Sonika went shopping with her daughter Arushi. She spent 2 of what she had on buying socks for
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Arushi and gave ` 2 to a beggar. She spent 2 of what was left on lunch and gave ` 10 as tip. She
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spent of the remaining amount for buying stationary for her daughter and spent ` 6 as bus fare.
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When they reached home, Sonika had ` 20 left in her purse. How much money did she take for
shopping?
12. Aishwarya is twice as old as Karishma. If six years is subtracted from Karishma’s age and four years
added to Aishwarya’s age, then Aishwarya will be 4 times Karishma’s age. How old were they two
years ago?
13. In a competitive exam, there are 90 multiple choice questions. 4 marks are awarded for every correct
answer, 2 marks are deducted for every wrong answer and 0.5 marks is deducted for every unattempted
question from the total score of correct answers. If a student leaves 10 questions unattempted and
scores a total of 195 marks, how many of his answers were correct?
14. A labourer was engaged for 30 days on the condition that he will get ` 60 for each day he works and
will be fined ` 10 for each day he is absent. If he gets ` 1,700 at the end of the month, for how many
days did he remain absent?
15. Sunny has three boxes of different types of sweets. Box I weighs 2 1 kg more than Box II and
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Box III weighs 10 kg more than Box II. The total weight of the boxes is 54 kg. What is the
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weight of Box I?

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