Q1. Three numbers A, B and C are in the ratio of 12 : 15 : 25. If sum of these numbers is 312, find the ratio between the difference of B and A and the difference of C and B.
(a) 3 : 7
(b) 10 : 3
(c) 3 : 10
(d) 7 : 3
(e) None of these
Q2. If A : B = 3/4, B : C = 4/5, C : D = 5/6, then A : D will be:
(a) 2 : 3
(b) 4 : 3
(c) 1 : 2
(d) 2 : 1
(e) None of these
S2. Ans.(c)
Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6
∴A∶B∶C∶D= 3 : 4 : 5 : 6.
Thus, A : D = 3 : 6 or, 1 : 2.
Q3. The ratio of present ages of Suresh and Mahesh is 7 : 5. If after 6 years their ages will be in the ratio of 4 : 3, the present age of Mahesh is:
(a) 32 years
(b) 36 years
(c) 30 years
(d) 35 years
(e) None of these
Q4. In a mixture of 60 litres, the ratio of milk and water is 2 : 1. What amount of water must be added to make the ratio of milk and water as 1 : 2?
(a) 75 litres
(b) 55 litres
(c) 60 litres
(d) 65 litres
(e) None of these
S4. Ans.(c)
Sol. Here, milk = 40, water = 20
Let x litres of water is added
(20+x)/(60+x) = 2/3
x = 60 litres
Q5. Mixture of milk and water has been kept in two separate containers. Ratio of milk to water in one of the containers is 5 : 1 and that in the other container 7 : 2. In what ratio the mixtures of these two containers should be added together so that the quantity of milk in the new mixture may become 80%?
(a) 2 : 3
(b) 3 : 2
(c) 4 : 5
(d) 1 : 3
(e) None of these
Q6. Seven men, five women and eight children were given as assignment of distributing 2000 books to students in a school over a period of three days. All of them distributed books on the first day. One of the second day two women and three children remained absent and on the third day three men and five children remained absent. If the ratio of the number of books distributed in a day by a man, a woman and a child was 5 : 4 : 2 respectively, a total of approximately how many books were distributed on the second day?
(a) 1000
(b) 800
(c) 650
(d) 900
(e) Cannot be determined
S6. Ans.(c)
Sol. Let the books distributed by man, a woman and a child be 5x, 4x and 2x respectively.
∴ No. of books distributed in 1st day
= 7×5x+5×4x+8×2x=71x
No. of books distributed in 1Ind day
=7×5x+3×4x+5×2x=57x
And no. of books distributed in IIIrd day
=4×5x+5×4x+3×2x=46x
71x + 57x + 46x = 2000, x = 2000/174
57x=2000/174×57=650 (Approx.)
Q7. A sum of money is divided among A, B, C and D in the ratio 3 : 5 : 8 : 9 respectively. If the share of D Rs. 1,872 more than the share of A, then what is the total amount of money of B & C together?
(a) Rs. 4,156
(b) Rs. 4,165
(c) Rs.4,056
(d) Rs. 4,065
(e) None of these
Q8. The ratio of the incomes of two persons is 5 : 3 and that of their expenditure is 9 : 5. If they save Rs. 2600 and Rs. 1800 respectively, then their incomes are:
(a) Rs. 8000, Rs. 4800
(b) Rs. 6000, Rs. 3600
(c) Rs. 10000, Rs.60000
(d) Rs. 9000, Rs. 5400
(e) None of these
Q9. A bag contains one rupee, 50 paise and 25 paise coins in the ratio 2 : 3 : 5. Their total value is Rs. 144. The value of 50-paise coins is:
(a) Rs. 24
(b) Rs. 36
(c) Rs. 48
(d) Rs. 72
(e) None of these
S9. Ans.(b)
Sol. Let the number of one-rupee coins, 50-paise coins and 25-paise coins be 2k, 3k and 5k, respectively.
∴ 2k × 1 + 3k × 0.50 + 5k × 0.25 = 114
⇒ 2k + 1.50k + 1.25k = 114
⇒ 4.75k = 114
⇒ k = 24.
50 paise value = 1.5x = 1.5*24 = 36
Q10. Two numbers are in the ratio 1(1/2) ∶2(2/3). When each of these is increased by 15, they become in the ratio 1(2/3) ∶2(1/2). The greater of the numbers is:
(a) 27
(b) 36
(c) 48
(d) 64
(e) None of these
Q11. Determine the ratio of the number of people having characteristic X to the number of people having characteristic Y in a population of 100 subjects from the following table:
Having X and Y - 10
Having X but not Y - 30
Having Y but not X - 20
Having neither X nor Y - 40
(a) 4 : 3
(b) 3 : 2
(c) 1 : 2
(d) 2 : 3
(e) None of these
S11. Ans.(a)
Sol. Number of people having characteristic X
= 10 + 30 = 40
Number of people having characteristic Y
= 10 + 20 = 30
Required ratio = 40 : 30 = 4 : 3
Q12. The incomes of A, B and C are in the ratio 7 : 9 : 12 and their spending are in the ratio 8 : 9 : 15. If A saves one-fourth of his income, then the savings of A, B and C are in the ratio of:
(a) 69 : 56 : 48
(b) 47 : 74 : 99
(c) 37 : 72 : 49
(d) 56 : 99 : 69
(e) None of these
Q13. The students in three classes are in the ratio 4 : 6 : 9. If 12 students are increased in each class, the ratio changes to 7 : 9 : 12. Then the total number of students in the three classes before the increase is:
(a) 95
(b) 76
(c) 100
(d) 114
(e) None of these
S13. Ans.(b)
Sol. Let the original number of students be 4x, 6x and 9x.
Now, according to the question,
(4x + 12)/(6x + 12)=7/9
⇒ 42x + 84 = 36x + 108
⇒ 42x – 36x = 108 – 84
⇒ 6x = 24
⇒ x = 4
∴ Required number of students = 4x + 6x + 9x = 19x = 19 × 4 = 76
Q14. When X is subtracted from the numbers 9, 15 and 27, then remainders are in the continued proportion. What is the value of X?
(a) 8
(b) 6
(c) 4
(d) 5
(e) None of these
S14. Ans.(e)
Sol. Let x be subtracted from the numbers 9, 15 and 27 we get continue proportion.
Now, (9 – x) : (15 – x) : (27– x)
∴ b^2=ac
⇒ (15-x)^2=(9-x)(27-x)
Or, 225 – 30x +x^2=243+x^2-36x
Or 6x = 243 – 225 = 18
∴ x = 3
Hence, number become 9 – x = 9 – 3 = 6
15 – x = 15 – 3 = 12
And, 27 – x = 27 – 3 = 24
∴ 6 : 12 : 24 = 1 : 2 : 4
Q15. A certain amount was to be distributed among A, B and C in the ratio 2 : 3 : 4, but was erroneously distributed in the ratio 7 : 2 : 5. As a result of this, B received Rs. 40 less. What is the actual amount?
(a) Rs. 210
(b) Rs. 270
(c) Rs. 230
(d) Rs. 280
(e) None of these
