Ratio, Proportion
- Two numbers are in the ratio 7 : 11. If 7 is added to each of the numbers, the ratio becomes
2 : 3. The smaller number is
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Let the numbers be 7x and 11x respectively.
∴ 7x + 7 = 2 11x + 7 3
∴ 22x + 14 = 21x + 21
⇒ x = 7
∴ Smaller number
= 7x = 7 × 7 = 49
Second Method :
Here, a = 7, b = 11, x = 7, c= 2, d = 31st Number= xa(c − d) ad − bc = 7 × 7(2 − 3) 7 × 3 − 11 × 2 = 49 × −1 = 49 21 − 22 2nd Number = xb(c − d) ad − bc = 7 × 11(2 − 3) 7 × 3 − 11 × 2 = 77 × −1 = 77 21 − 22
∴ Smallest number = 49Correct Option: B
Let the numbers be 7x and 11x respectively.
∴ 7x + 7 = 2 11x + 7 3
∴ 22x + 14 = 21x + 21
⇒ x = 7
∴ Smaller number
= 7x = 7 × 7 = 49
Second Method :
Here, a = 7, b = 11, x = 7, c= 2, d = 31st Number= xa(c − d) ad − bc = 7 × 7(2 − 3) 7 × 3 − 11 × 2 = 49 × −1 = 49 21 − 22 2nd Number = xb(c − d) ad − bc = 7 × 11(2 − 3) 7 × 3 − 11 × 2 = 77 × −1 = 77 21 − 22
∴ Smallest number = 49
- What must be added to each term of the ratio 7 : 11, so as to make it equal to 3 : 4 ?
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Let the required number be x.
∴ 7 + x = 3 11 + x 4
⇒ 28 + 4x = 33 + 3x
⇒ x = 33 – 28 = 5Correct Option: D
Let the required number be x.
∴ 7 + x = 3 11 + x 4
⇒ 28 + 4x = 33 + 3x
⇒ x = 33 – 28 = 5
- The number of students in three classes are in the ratio 2 : 3 : 4. If 12 students are increased in each class, this ratio changes to 8 : 11 :14. The total number of students in the three classes at the beginning was
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Let the original number of students be 2x, 3x and 4x in three class.
According to the question,2x + 12 = 8 3x + 12 11
⇒ 24x + 96 = 22x + 132
⇒ 2x = 132 – 96 = 36⇒ x = 36 = 18 2
∴ Original number of students
= 2x + 3x + 4x
= 9x = 9 × 18 = 162Correct Option: A
Let the original number of students be 2x, 3x and 4x in three class.
According to the question,2x + 12 = 8 3x + 12 11
⇒ 24x + 96 = 22x + 132
⇒ 2x = 132 – 96 = 36⇒ x = 36 = 18 2
∴ Original number of students
= 2x + 3x + 4x
= 9x = 9 × 18 = 162
- In a school having roll strength 286, the ratio of boys and girls is 8 : 5. If 22 more girls get admitted into the school, the ratio of boys and girls becomes
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Initially number of boys
= 8 × 286 = 8 × 286 = 176 8 + 5 13
∴ Number of girls= 5 × 286 = 110 13
22 more girls get admitted.
∴ Required ratio= 176 = 176 = 4 110 + 22 132 3
= 4 : 3Correct Option: D
Initially number of boys
= 8 × 286 = 8 × 286 = 176 8 + 5 13
∴ Number of girls= 5 × 286 = 110 13
22 more girls get admitted.
∴ Required ratio= 176 = 176 = 4 110 + 22 132 3
= 4 : 3
- The ratio of the number of ladies to that of gents at a party was 3 : 2. When 20 more gents joined the party, the ratio was reversed. The number of ladies present at the party was
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Let the number of ladies and gents be 3x and 2x respectively.
According to the question,3x = 2 2x + 20 3
⇒ 9x = 4x + 40 ⇒ 5x = 40
⇒ 9x = 4x + 40 ⇒ 5x = 40
⇒ x = 8
∴ Number of ladies = 3x
= 3 × 8 = 24Correct Option: C
Let the number of ladies and gents be 3x and 2x respectively.
According to the question,3x = 2 2x + 20 3
⇒ 9x = 4x + 40 ⇒ 5x = 40
⇒ 9x = 4x + 40 ⇒ 5x = 40
⇒ x = 8
∴ Number of ladies = 3x
= 3 × 8 = 24
