Problems on Numbers: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 2)

Let the number be x. 1/5 of 1/6 of x equals 12. So 1/5 × 1/6 × x = 12, which is 1/30x = 12. Solving gives x = 12 / (1/30) = 360. Now find 2/5 of x: 2/5 × 360 = 144. Check: 1/5 × 1/6 × 360 = 1/30 × 360 = 12, which matches.

Let the number be x. 1/2 of 1/4 of x equals 23. So 1/2 × 1/4 × x = 23, which is 1/8x = 23. Solving gives x = 23 / (1/8) = 184. Now find 3/4 of x: 3/4 × 184 = 138. Check: 1/2 × 1/4 × 184 = 1/8 × 184 = 23, which matches.

Let the number be x. 1/5 of 1/2 of x equals 27. So 1/5 × 1/2 × x = 27, which is 1/10x = 27. Solving gives x = 27 / (1/10) = 270. Now find 1/2 of x: 1/2 × 270 = 135. Check: 1/5 × 1/2 × 270 = 1/10 × 270 = 27, which matches.

Let the number be x. 1/3 of 1/6 of x equals 20. So 1/3 × 1/6 × x = 20, which is 1/18x = 20. Solving gives x = 20 / (1/18) = 360. Now find 1/2 of x: 1/2 × 360 = 180. Check: 1/3 × 1/6 × 360 = 1/18 × 360 = 20, which matches.

Let the number be x. 1/5 of 1/2 of x equals 25. So 1/5 × 1/2 × x = 25, which is 1/10x = 25. Solving gives x = 25 / (1/10) = 250. Now find 2/5 of x: 2/5 × 250 = 100. Check: 1/5 × 1/2 × 250 = 1/10 × 250 = 25, which matches.

Let the number be x. 1/2 of 1/4 of x equals 16. So 1/2 × 1/4 × x = 16, which is 1/8x = 16. Solving gives x = 16 / (1/8) = 128. Now find 3/4 of x: 3/4 × 128 = 96. Check: 1/2 × 1/4 × 128 = 1/8 × 128 = 16, which matches.

Let the number be x. 1/6 of 1/6 of x equals 17. So 1/6 × 1/6 × x = 17, which is 1/36x = 17. Solving gives x = 17 / (1/36) = 612. Now find 3/4 of x: 3/4 × 612 = 459. Check: 1/6 × 1/6 × 612 = 1/36 × 612 = 17, which matches.

Let the number be x. 1/2 of 1/3 of x equals 32. So 1/2 × 1/3 × x = 32, which is 1/6x = 32. Solving gives x = 32 / (1/6) = 192. Now find 3/4 of x: 3/4 × 192 = 144. Check: 1/2 × 1/3 × 192 = 1/6 × 192 = 32, which matches.

Let the number be x. Twice the number plus three times 19 equals 181. So 2x + 3×19 = 181. That gives 2x = 181 – 57 = 124. Solving gives x = 124 / 2 = 62. Now find thrice the number plus two times 19: 3×62 + 2×19 = 186 + 38 = 224. Check: 2×62 + 3×19 = 124 + 57 = 181, which matches the given sum.

Let the number be x. Twice the number plus three times 50 equals 252. So 2x + 3×50 = 252. That gives 2x = 252 – 150 = 102. Solving gives x = 102 / 2 = 51. Now find thrice the number plus two times 50: 3×51 + 2×50 = 153 + 100 = 253. Check: 2×51 + 3×50 = 102 + 150 = 252, which matches the given sum.

Let the number be x. Twice the number plus three times 55 equals 311. So 2x + 3×55 = 311. That gives 2x = 311 – 165 = 146. Solving gives x = 146 / 2 = 73. Now find thrice the number plus two times 55: 3×73 + 2×55 = 219 + 110 = 329. Check: 2×73 + 3×55 = 146 + 165 = 311, which matches the given sum.

Let the number be x. Twice the number plus three times 33 equals 265. So 2x + 3×33 = 265. That gives 2x = 265 – 99 = 166. Solving gives x = 166 / 2 = 83. Now find thrice the number plus two times 33: 3×83 + 2×33 = 249 + 66 = 315. Check: 2×83 + 3×33 = 166 + 99 = 265, which matches the given sum.

Let the number be x. Twice the number plus three times 55 equals 283. So 2x + 3×55 = 283. That gives 2x = 283 – 165 = 118. Solving gives x = 118 / 2 = 59. Now find thrice the number plus two times 55: 3×59 + 2×55 = 177 + 110 = 287. Check: 2×59 + 3×55 = 118 + 165 = 283, which matches the given sum.

Let the number be x. Twice the number plus three times 39 equals 303. So 2x + 3×39 = 303. That gives 2x = 303 – 117 = 186. Solving gives x = 186 / 2 = 93. Now find thrice the number plus two times 39: 3×93 + 2×39 = 279 + 78 = 357. Check: 2×93 + 3×39 = 186 + 117 = 303, which matches the given sum.

Let the number be x. Twice the number plus three times 48 equals 240. So 2x + 3×48 = 240. That gives 2x = 240 – 144 = 96. Solving gives x = 96 / 2 = 48. Now find thrice the number plus two times 48: 3×48 + 2×48 = 144 + 96 = 240. Check: 2×48 + 3×48 = 96 + 144 = 240, which matches the given sum.

Let the number be x. Twice the number plus three times 31 equals 233. So 2x + 3×31 = 233. That gives 2x = 233 – 93 = 140. Solving gives x = 140 / 2 = 70. Now find thrice the number plus two times 31: 3×70 + 2×31 = 210 + 62 = 272. Check: 2×70 + 3×31 = 140 + 93 = 233, which matches the given sum.

Let the number be x. Multiplying it by 14 increases it by 390. So 14x = x + 390. That simplifies to (14 – 1)x = 390. Solving gives x = 390 / 13 = 30. Check: 14 × 30 = 420, and 420 – 30 = 390, which matches.

Let the number be x. Multiplying it by 10 increases it by 558. So 10x = x + 558. That simplifies to (10 – 1)x = 558. Solving gives x = 558 / 9 = 62. Check: 10 × 62 = 620, and 620 – 62 = 558, which matches.

Let the number be x. Multiplying it by 14 increases it by 1027. So 14x = x + 1027. That simplifies to (14 – 1)x = 1027. Solving gives x = 1027 / 13 = 79. Check: 14 × 79 = 1106, and 1106 – 79 = 1027, which matches.

Let the number be x. Multiplying it by 19 increases it by 180. So 19x = x + 180. That simplifies to (19 – 1)x = 180. Solving gives x = 180 / 18 = 10. Check: 19 × 10 = 190, and 190 – 10 = 180, which matches.

Let the number be x. Multiplying it by 19 increases it by 594. So 19x = x + 594. That simplifies to (19 – 1)x = 594. Solving gives x = 594 / 18 = 33. Check: 19 × 33 = 627, and 627 – 33 = 594, which matches.

Let the number be x. Multiplying it by 12 increases it by 539. So 12x = x + 539. That simplifies to (12 – 1)x = 539. Solving gives x = 539 / 11 = 49. Check: 12 × 49 = 588, and 588 – 49 = 539, which matches.

Let the number be x. Multiplying it by 16 increases it by 885. So 16x = x + 885. That simplifies to (16 – 1)x = 885. Solving gives x = 885 / 15 = 59. Check: 16 × 59 = 944, and 944 – 59 = 885, which matches.

Let the number be x. Multiplying it by 11 increases it by 300. So 11x = x + 300. That simplifies to (11 – 1)x = 300. Solving gives x = 300 / 10 = 30. Check: 11 × 30 = 330, and 330 – 30 = 300, which matches.

Let the number be x. Multiplying it by 19 increases it by 810. So 19x = x + 810. That simplifies to (19 – 1)x = 810. Solving gives x = 810 / 18 = 45. Check: 19 × 45 = 855, and 855 – 45 = 810, which matches.