Ratio, Proportion
- A and B together have ₹ 158. C has ₹ 101 less than what A and B together have, and B has ₹ 23 more than C. The amount of A is :
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A + B = 158
C = 158 – 101 = 57
Also B = 57 + 23 = 80
∴ The amount with A
= ₹ (158 – 80) = ₹ 78Correct Option: B
A + B = 158
C = 158 – 101 = 57
Also B = 57 + 23 = 80
∴ The amount with A
= ₹ (158 – 80) = ₹ 78
- A man leaves ₹ 8,600 to be divided among 5 sons, 4 daughters and 2 nephews. If each daughter receives four times as much as each nephew and each son receives five times as much as each nephew, how much does each daughter receive?
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According to question,
Son : Daughter : Nephew
= 5x : 4x : x
But 5 sons : 4 daughters : 2 nephews
= 25x : 16x : 2x
and 25x + 16x + 2x = ₹ 8600
43x = ₹ 8600
x = ₹ 200
∴ Required answer
= 4 × 200 = ₹ 800Correct Option: C
According to question,
Son : Daughter : Nephew
= 5x : 4x : x
But 5 sons : 4 daughters : 2 nephews
= 25x : 16x : 2x
and 25x + 16x + 2x = ₹ 8600
43x = ₹ 8600
x = ₹ 200
∴ Required answer
= 4 × 200 = ₹ 800
- The price of a refrigerator and a television set are in the ratio 5 : 3. If the refrigerator costs ₹ 5500 more than the television set, then the price of the refrigerator is:
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CP of refrigerator = ₹ 5x
CP of television = ₹ 3x
∴ 2x = 5500⇒ x = 5500 = 2750 2
∴ CP of refrigerator
= 5 × 2750 = ₹ 13750Correct Option: C
CP of refrigerator = ₹ 5x
CP of television = ₹ 3x
∴ 2x = 5500⇒ x = 5500 = 2750 2
∴ CP of refrigerator
= 5 × 2750 = ₹ 13750
- The ratio of the numbers of boys and girls in a school was 5 : 3. Some new boys and girls were admitted to the school, in the ratio 5 : 7. At this, the total number of students in the school became 1200, and the ratio of boys to girls changed to 7 : 5. The number of students in the school before new admissions was
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Let the original number of boys and girls be 5x and 3x respectively and that of new boys and girls be 5y and 7y respectively.
∴ 5x + 3x + 5y + 7y = 1200
⇒ 2x + 3y = 300 ............(i)and, 5x + 5y = 7 3x + 7y 5
⇒ 25x + 25y = 21x + 49y
⇒ 4x = 24y
⇒ x = 6y ......... (ii)
4x + 6y = 600
⇒ 5x = 600 ⇒ x = 120
∴ Original number of students
= 8x = 960Correct Option: D
Let the original number of boys and girls be 5x and 3x respectively and that of new boys and girls be 5y and 7y respectively.
∴ 5x + 3x + 5y + 7y = 1200
⇒ 2x + 3y = 300 ............(i)and, 5x + 5y = 7 3x + 7y 5
⇒ 25x + 25y = 21x + 49y
⇒ 4x = 24y
⇒ x = 6y ......... (ii)
4x + 6y = 600
⇒ 5x = 600 ⇒ x = 120
∴ Original number of students
= 8x = 960
- The weight of Mr. Gupta and Mrs. Gupta are in the ratio 7 : 8 and their total weight is 120 kg. After taking a dieting course Mr. Gupta reduces by 6 kg and the ratio between their weights changes to 5 : 6. So Mrs. Gupta has reduced by
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Let the initial weights of Mr. Gupta and Mrs. Gupta be 7x and 8x kg respectively.
∴ 7x + 8x = 120
⇒ 15x = 120⇒ x = 120 = 8 15
∴ Mr. Gupta’s weight = 7 × 8 = 56 kg
Mrs. Gupta’s weight = 8 × 8 = 64 kg
Let Mrs. Gupta reduce her weight by y kg.∴ 56 − 6 = 5 64 − y 6 ⇒ 50 = 5 64 − y 6
⇒ 64 – y = 60
⇒ y = 64 – 60 = 4 kgCorrect Option: B
Let the initial weights of Mr. Gupta and Mrs. Gupta be 7x and 8x kg respectively.
∴ 7x + 8x = 120
⇒ 15x = 120⇒ x = 120 = 8 15
∴ Mr. Gupta’s weight = 7 × 8 = 56 kg
Mrs. Gupta’s weight = 8 × 8 = 64 kg
Let Mrs. Gupta reduce her weight by y kg.∴ 56 − 6 = 5 64 − y 6 ⇒ 50 = 5 64 − y 6
⇒ 64 – y = 60
⇒ y = 64 – 60 = 4 kg
