Ratio, Proportion
- The average of 11 numbers is 36, whereas average of 9 of them is 34. If the remaining two numbers are in the ratio of 2 : 3, find the value of the smaller number (between remaining two numbers).
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According to the question,
Sum of remaining two numbers
= 11 × 36 – 9 × 34
= 396 – 306 = 90
Ratio of the remaining two numbers = 2 : 3∴ Smaller number = 2 × 90 = 36 5 Correct Option: D
According to the question,
Sum of remaining two numbers
= 11 × 36 – 9 × 34
= 396 – 306 = 90
Ratio of the remaining two numbers = 2 : 3∴ Smaller number = 2 × 90 = 36 5
- The ratio of number of boys to the number of girls in a school of 432 pupils is 5 : 4. When some new boys and girls are admitted, the number of boys increase by 12 and the ratio of the boys to girls changes to 7 : 6. The number of new girls admitted is
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Original number of boys in school = 5 × 432 = 240 9
Number of girls = 432 – 240 = 192
Let the new number of girls be x.
According to the question,240 + 12 = 7 192 + x 6 ⇒ 252 = 7 192 + x 6
⇒ 192 × 7 + 7x = 252 × 6
⇒ 1344 + 7x = 1512
⇒ 7x = 1512 – 1344 = 168⇒ x = 168 = 24 7 Correct Option: C
Original number of boys in school = 5 × 432 = 240 9
Number of girls = 432 – 240 = 192
Let the new number of girls be x.
According to the question,240 + 12 = 7 192 + x 6 ⇒ 252 = 7 192 + x 6
⇒ 192 × 7 + 7x = 252 × 6
⇒ 1344 + 7x = 1512
⇒ 7x = 1512 – 1344 = 168⇒ x = 168 = 24 7
- If the ratio of two numbers is 1 : 5 and their product is 320, then the difference between the squares of these two numbers is :
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Let the numbers be x and 5x.
According to the question,
x × 5x = 320
⇒ 5x2 = 320⇒ x2 = 320 = 64 5
⇒ x = √64 = 8
∴ Required difference
= (5x)2 – x2
= 25x2 – x2 = 24x2
= 24 × 8 × 8 = 1536Correct Option: C
Let the numbers be x and 5x.
According to the question,
x × 5x = 320
⇒ 5x2 = 320⇒ x2 = 320 = 64 5
⇒ x = √64 = 8
∴ Required difference
= (5x)2 – x2
= 25x2 – x2 = 24x2
= 24 × 8 × 8 = 1536
- The ratio of two positive numbers is 3 : 4. The sum of their squares is 400. What is the sum of the numbers ?
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Let two positive numbers be 3x and 4x.
According to the question,
(3x)2 + (4x)2 = 400
⇒ 9x2 + 16x2 = 400
⇒ 25x2 = 400⇒ x2 = 400 = 16 25
⇒ x = √16 = 4
∴ Sum of numbers
= 3x + 4x = 7x
= 7 × 4 = 28Correct Option: A
Let two positive numbers be 3x and 4x.
According to the question,
(3x)2 + (4x)2 = 400
⇒ 9x2 + 16x2 = 400
⇒ 25x2 = 400⇒ x2 = 400 = 16 25
⇒ x = √16 = 4
∴ Sum of numbers
= 3x + 4x = 7x
= 7 × 4 = 28
- Three numbers are in the ratio 1 : 2 : 3 and the sum of their cubes is 4500 . The smallest number is
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Let the numbers be x, 2x and 3x.
According to the question,
x3 + (2x)3 + (3x)3 = 4500
⇒ x3 + 8x3 + 27x3 = 4500
⇒ 36x3 = 4500⇒ x3 = 4500 = 125 36
∴ x3 = √125
= 5 = smallest numberCorrect Option: B
Let the numbers be x, 2x and 3x.
According to the question,
x3 + (2x)3 + (3x)3 = 4500
⇒ x3 + 8x3 + 27x3 = 4500
⇒ 36x3 = 4500⇒ x3 = 4500 = 125 36
∴ x3 = √125
= 5 = smallest number
