This lesson gives each rule, the reason it works and seven worked examples. It also lists the traps that cost marks.
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Q1. If a number is added to three-fifths of itself, the result is 408. What is the number?
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Answer: A
Let the number be x. The number plus 3/5 of itself equals 408. So x + 3/5x = 408. That simplifies to (8/5)x = 408. Solving gives x = 408 / (8/5) = 255. Check: 3/5 of 255 is 153, and 255 + 153 = 408, which matches.
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Q2. If a number is added to three-fourths of itself, the result is 616. What is the number?
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Answer: D
Let the number be x. The number plus 3/4 of itself equals 616. So x + 3/4x = 616. That simplifies to (7/4)x = 616. Solving gives x = 616 / (7/4) = 352. Check: 3/4 of 352 is 264, and 352 + 264 = 616, which matches.
Related topics: Problems on Numbers: Formulas, Shortcuts and Solved Examples
Q3. If a number is added to three-fifths of itself, the result is 1080. What is the number?
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Answer: C
Let the number be x. The number plus 3/5 of itself equals 1080. So x + 3/5x = 1080. That simplifies to (8/5)x = 1080. Solving gives x = 1080 / (8/5) = 675. Check: 3/5 of 675 is 405, and 675 + 405 = 1080, which matches.
Related topics: Problems on Numbers: Formulas, Shortcuts and Solved Examples
Q4. If a number is added to two-sevenths of itself, the result is 603. What is the number?
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Answer: B
Let the number be x. The number plus 2/7 of itself equals 603. So x + 2/7x = 603. That simplifies to (9/7)x = 603. Solving gives x = 603 / (9/7) = 469. Check: 2/7 of 469 is 134, and 469 + 134 = 603, which matches.
Related topics: Problems on Numbers: Formulas, Shortcuts and Solved Examples
Q5. The difference between a number and three-eighths of it is 995. What is the number?
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Answer: D
Let the number be x. The number minus 3/8 of itself is 995. So x – 3/8x = 995. That simplifies to (5/8)x = 995. Solving gives x = 995 / (5/8) = 1592. Check: 3/8 of 1592 is 597, and 1592 – 597 = 995, which matches.
Related topics: Problems on Numbers: Formulas, Shortcuts and Solved Examples
Q6. The difference between a number and three-fifths of it is 330. What is the number?
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Answer: A
Let the number be x. The number minus 3/5 of itself is 330. So x – 3/5x = 330. That simplifies to (2/5)x = 330. Solving gives x = 330 / (2/5) = 825. Check: 3/5 of 825 is 495, and 825 – 495 = 330, which matches.
Related topics: Problems on Numbers: Formulas, Shortcuts and Solved Examples
Q7. The difference between a number and three-eighths of it is 980. What is the number?
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Answer: C
Let the number be x. The number minus 3/8 of itself is 980. So x – 3/8x = 980. That simplifies to (5/8)x = 980. Solving gives x = 980 / (5/8) = 1568. Check: 3/8 of 1568 is 588, and 1568 – 588 = 980, which matches.
Related topics: Problems on Numbers: Formulas, Shortcuts and Solved Examples
Q8. The difference between a number and one-tenth of it is 261. What is the number?
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Answer: D
Let the number be x. The number minus 1/10 of itself is 261. So x – 1/10x = 261. That simplifies to (9/10)x = 261. Solving gives x = 261 / (9/10) = 290. Check: 1/10 of 290 is 29, and 290 – 29 = 261, which matches.
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Q9. The difference between a number and one-seventh of it is 504. What is the number?
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Answer: A
Let the number be x. The number minus 1/7 of itself is 504. So x – 1/7x = 504. That simplifies to (6/7)x = 504. Solving gives x = 504 / (6/7) = 588. Check: 1/7 of 588 is 84, and 588 – 84 = 504, which matches.
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Q10. The difference between a number and four-fifths of it is 167. What is the number?
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Answer: B
Let the number be x. The number minus 4/5 of itself is 167. So x – 4/5x = 167. That simplifies to (1/5)x = 167. Solving gives x = 167 / (1/5) = 835. Check: 4/5 of 835 is 668, and 835 – 668 = 167, which matches.
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Q11. The difference between a number and one-tenth of it is 207. What is the number?
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Answer: A
Let the number be x. The number minus 1/10 of itself is 207. So x – 1/10x = 207. That simplifies to (9/10)x = 207. Solving gives x = 207 / (9/10) = 230. Check: 1/10 of 230 is 23, and 230 – 23 = 207, which matches.
Related topics: Problems on Numbers: Formulas, Shortcuts and Solved Examples
Q12. The difference between a number and four-fifths of it is 155. What is the number?
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Answer: B
Let the number be x. The number minus 4/5 of itself is 155. So x – 4/5x = 155. That simplifies to (1/5)x = 155. Solving gives x = 155 / (1/5) = 775. Check: 4/5 of 775 is 620, and 775 – 620 = 155, which matches.
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Q13. The difference between a number and four-fifths of it is 27. What is the number?
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Answer: C
Let the number be x. The number minus 4/5 of itself is 27. So x – 4/5x = 27. That simplifies to (1/5)x = 27. Solving gives x = 27 / (1/5) = 135. Check: 4/5 of 135 is 108, and 135 – 108 = 27, which matches.
Related topics: Problems on Numbers: Formulas, Shortcuts and Solved Examples
Q14. The difference between a number and one-third of it is 174. What is the number?
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Answer: D
Let the number be x. The number minus 1/3 of itself is 174. So x – 1/3x = 174. That simplifies to (2/3)x = 174. Solving gives x = 174 / (2/3) = 261. Check: 1/3 of 261 is 87, and 261 – 87 = 174, which matches.
Related topics: Problems on Numbers: Formulas, Shortcuts and Solved Examples