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Question 1 of 5
1. Question
Consider the following statements about the ages of A, B and C:
- The ratio of the age of A to B is 3 : 2 and the ratio of the age of B to C is 4 : 5.
- The average age of A, B and C is 27 years.
- C is 12 years older than B.
Which of the statements is/are sufficient to find the age of A?
Correct
Answer: (d)
Explanation:
From Statement 1, the ratios can be combined as A : B : C equals 6 : 4 : 5.
Let the ages of A, B and C be 6x, 4x and 5x respectively. Statement 1 alone is not sufficient because x is not known.Using Statement 2 with Statement 1, the average age is 27 years, so the total age is 81 years. Substituting the values gives 15x equals 81, which fixes x and hence the age of A.
Using Statement 3 with Statement 1, C is 12 years older than B. Substituting the values gives 5x equals 4x plus 12, which fixes x and hence the age of A.
Therefore, Statement 1 along with either Statement 2 or Statement 3 is sufficient.
Incorrect
Answer: (d)
Explanation:
From Statement 1, the ratios can be combined as A : B : C equals 6 : 4 : 5.
Let the ages of A, B and C be 6x, 4x and 5x respectively. Statement 1 alone is not sufficient because x is not known.Using Statement 2 with Statement 1, the average age is 27 years, so the total age is 81 years. Substituting the values gives 15x equals 81, which fixes x and hence the age of A.
Using Statement 3 with Statement 1, C is 12 years older than B. Substituting the values gives 5x equals 4x plus 12, which fixes x and hence the age of A.
Therefore, Statement 1 along with either Statement 2 or Statement 3 is sufficient.
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Question 2 of 5
2. Question
A sum of money is divided among P, Q, R and S in the ratio 2 : 3 : 5 : 8.
Statement I: If the share of R is ₹1,500, then the total sum can be determined.
Statement II: If S gets ₹900 more than Q, the share of P can be determined.Which of the above statement(s) is/are correct?
Correct
Answer: (c)
Explanation:
From the given ratio, let the shares of P, Q, R and S be 2x, 3x, 5x and 8x.- Using Statement I:
R’s share is 5x equals ₹1,500, so x is fixed. Once x is known, the total sum can be calculated. Hence, Statement I is correct. - Using Statement II:
S gets ₹900 more than Q, so 8x minus 3x equals 900. This gives x, and hence the share of P can be found. Statement II is also correct.
Therefore, both statements are correct.
Incorrect
Answer: (c)
Explanation:
From the given ratio, let the shares of P, Q, R and S be 2x, 3x, 5x and 8x.- Using Statement I:
R’s share is 5x equals ₹1,500, so x is fixed. Once x is known, the total sum can be calculated. Hence, Statement I is correct. - Using Statement II:
S gets ₹900 more than Q, so 8x minus 3x equals 900. This gives x, and hence the share of P can be found. Statement II is also correct.
Therefore, both statements are correct.
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Question 3 of 5
3. Question
The value of a diamond is directly proportional to the square of its weight. A diamond weighing 10 grams is worth ₹1,00,000. If the diamond breaks into two pieces whose weights are in the ratio 3 : 2, what is the total loss incurred?
Correct
Answer: (b)
Explanation:
Let the value of the diamond be proportional to the square of its weight.Original diamond:
Weight = 10 g
Value = ₹1,00,000So, value per unit = 1,00,000 ÷ (10²) = 1,00,000 ÷ 100 = 1,000
After breaking, weights are in ratio 3 : 2.
Total weight = 10 g, so pieces are 6 g and 4 g.Value of 6 g piece = 1,000 × 6² = 36,000
Value of 4 g piece = 1,000 × 4² = 16,000Total value after breaking = 36,000 + 16,000 = 52,000
Loss = Original value − New value
= 1,00,000 − 52,000 = ₹48,000Incorrect
Answer: (b)
Explanation:
Let the value of the diamond be proportional to the square of its weight.Original diamond:
Weight = 10 g
Value = ₹1,00,000So, value per unit = 1,00,000 ÷ (10²) = 1,00,000 ÷ 100 = 1,000
After breaking, weights are in ratio 3 : 2.
Total weight = 10 g, so pieces are 6 g and 4 g.Value of 6 g piece = 1,000 × 6² = 36,000
Value of 4 g piece = 1,000 × 4² = 16,000Total value after breaking = 36,000 + 16,000 = 52,000
Loss = Original value − New value
= 1,00,000 − 52,000 = ₹48,000 -
Question 4 of 5
4. Question
In a library, the ratio of the number of English books to Hindi books was 7 : 2. After the library purchased 500 more English books and 500 more Hindi books, the ratio became 5 : 2.
What was the original number of Hindi books in the library?Correct
Answer: (b)
Explanation:
Let the original numbers of English and Hindi books be 7x and 2x.After purchase:
English books = 7x + 500
Hindi books = 2x + 500Given new ratio:
(7x + 500) : (2x + 500) = 5 : 2So,
2(7x + 500) = 5(2x + 500)
14x + 1000 = 10x + 2500
4x = 1500
x = 375Original number of Hindi books = 2x = 2 × 375 = 750
Incorrect
Answer: (b)
Explanation:
Let the original numbers of English and Hindi books be 7x and 2x.After purchase:
English books = 7x + 500
Hindi books = 2x + 500Given new ratio:
(7x + 500) : (2x + 500) = 5 : 2So,
2(7x + 500) = 5(2x + 500)
14x + 1000 = 10x + 2500
4x = 1500
x = 375Original number of Hindi books = 2x = 2 × 375 = 750
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Question 5 of 5
5. Question
The ratio of the incomes of P, Q and R is 5 : 6 : 8. Their incomes are increased by 20%, 10% and 25% respectively. Find the new ratio of their incomes.
Correct
Answer: (b)
Explanation:
Let the original incomes be 5x, 6x and 8x.After increase:
P = 5x × 120/100 = 6x
Q = 6x × 110/100 = 6.6x
R = 8x × 125/100 = 10xNew ratio:
6 : 6.6 : 10Multiply by 5 to clear decimals:
30 : 33 : 50Incorrect
Answer: (b)
Explanation:
Let the original incomes be 5x, 6x and 8x.After increase:
P = 5x × 120/100 = 6x
Q = 6x × 110/100 = 6.6x
R = 8x × 125/100 = 10xNew ratio:
6 : 6.6 : 10Multiply by 5 to clear decimals:
30 : 33 : 50
