Ratio, Proportion
- The students in three classes are in the ratio 2 : 3 : 5. If 40 students are increased in each class, the ratio changes to 4 : 5 : 7. Originally, the total number of students was :
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Let the number of students in three classes be 2x, 3x and 5x respectively.
Due to increase of 40 students in each class, we have= 2x + 40 = 4 3x + 40 5
⇒ 10x + 200 = 12x + 160
⇒ 2x = 200 – 160 ⇒ 2x = 40
⇒ x = 20
∴ Original strength
= 10x = 10 × 20 = 200Correct Option: C
Let the number of students in three classes be 2x, 3x and 5x respectively.
Due to increase of 40 students in each class, we have= 2x + 40 = 4 3x + 40 5
⇒ 10x + 200 = 12x + 160
⇒ 2x = 200 – 160 ⇒ 2x = 40
⇒ x = 20
∴ Original strength
= 10x = 10 × 20 = 200
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Two numbers are in the ratio 1 1 : 2 2 . 2 3
The greater of the numbers is :Three numbers are in the ratio 1 : 2 : 3 . 2 3 4
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Let the numbers be
3 x and 8 x 2 3
According to question,= 3 x + 15 (5/3)/(5/2) 2 8x + 5 3 ⇒ 3x + 30 = 2/3 2 8x + 45 3 ⇒ 3(3x + 30) = 2 2(8x + 45) 3 ⇒ 9x + 90 = 2 16x + 90 3
⇒ 27x + 270 = 32x + 180
⇒ 32x – 27x = 270 – 180 = 90
⇒ 5x = 90 ⇒ x = 18
∴ The greater number= 8 x = 8 × 18 = 48 3 3 Correct Option: C
Let the numbers be
3 x and 8 x 2 3
According to question,= 3 x + 15 (5/3)/(5/2) 2 8x + 5 3 ⇒ 3x + 30 = 2/3 2 8x + 45 3 ⇒ 3(3x + 30) = 2 2(8x + 45) 3 ⇒ 9x + 90 = 2 16x + 90 3
⇒ 27x + 270 = 32x + 180
⇒ 32x – 27x = 270 – 180 = 90
⇒ 5x = 90 ⇒ x = 18
∴ The greater number= 8 x = 8 × 18 = 48 3 3
- The ratio of the number of boys and girls of a school with 504 students is 13 : 11. What will be the new ratio if 12 more girls are admitted?
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Total numbers of girls in the school
= 504 × 11 13 + 11 = 504 × 11 = 231 24
Total numbers of boys in the school= 504 × 13 13 + 11 = 504 × 13 = 273 29
Now, total no. of girls when 12 more girls are admitted
= 231 + 12 = 243
∴ Required ratio = 273 : 243 = 91 : 81Correct Option: A
Total numbers of girls in the school
= 504 × 11 13 + 11 = 504 × 11 = 231 24
Total numbers of boys in the school= 504 × 13 13 + 11 = 504 × 13 = 273 29
Now, total no. of girls when 12 more girls are admitted
= 231 + 12 = 243
∴ Required ratio = 273 : 243 = 91 : 81
- A and B have money in the ratio 2 : 1. If A gives ₹ 2 to B, the money will be in the ratio 1 : 1.
What were the initial amounts they had?
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Let A and B have ₹ 2x and ₹ x initially.
∴ 2x–2 = x + 2
⇒ x = 4
∴ Initial amount with A = ₹ 8
∴ Initial amount with B = ₹ 4.Correct Option: C
Let A and B have ₹ 2x and ₹ x initially.
∴ 2x–2 = x + 2
⇒ x = 4
∴ Initial amount with A = ₹ 8
∴ Initial amount with B = ₹ 4.
- The ratio of two numbers is 3 : 4 and their HCF is 15. Then the sum of the two numbers is :
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Let the numbers be 3x and 4x.
Their HCF = x = 15
∴ Sum of numbers = 3x + 4x = 7x = 15 × 7 = 105Correct Option: A
Let the numbers be 3x and 4x.
Their HCF = x = 15
∴ Sum of numbers = 3x + 4x = 7x = 15 × 7 = 105
