### RATIO AND PROPORTION QUIZ 001

- Out of the total 390 students studying in a college of Arts and Science, boys and girls are in the ratio of 7 : 6 respectively and the number of students studying Arts and Science are in the ratio of 3 : 7 respectively. The boys and girls studying Arts are in the ratio of 4 : 5 respectively. How many boys are studying Science?

(a) 52

(b) 65

(c) 115

**(d) 158**

(e) None of these

Explanation:

Given, boys and girls are in the ratio of 7 : 6,

So, Number of boys = 7/13 x 390 = 210

Number of girls = 390 – 210 = 180

Students studying Arts and Science are in the ratio of 3 : 7,

Number of students studying Arts = 3/10 x 390 = 117

Number of students studying Science = 390 – 117 = 273

Also boys and girls studying Arts are in the ratio of 4 : 5,

Number of boys studying arts = 4/9 x 117 = 52

Number of boys studying science = 210 – 52 = 158

- From a number of mangoes, a man sells half the number of existing mangoes plus 1 to the first customer, then sells 1/3rd of the remaining number of mangoes plus 1 to the second customer, then 1/4th of the remaining number of mangoes plus 1 to the third customer and 1/5th of the remaining number of mangoes plus 1 to the fourth customer. He then finds that he does not have any mangoes left. How many mangoes did he have originally?

(a) 12

(b) 14

(c) 15

(d) 13

(e) None of these

Explanation:

Let the No. of mangoes that the man had originally = X

No. of mangoes sold balance

1st customer = (X/2) + 1 (X – 2)/2

2nd customer = (X – 2)/6 + 1 (X – 5)/3

3rd customer = (X – 5)/12 + 1 (X – 9)/4

4th customer = (X – 9)/20 + 1 0

(X – 9)/20 + 1= (X – 9)/4 => X = 14

3. Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

**(a) 2:3:4**

(b) 6:7:8

(c) 6:8:9

(d) 7:8:9

(e) None of these

Explanation:

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.

Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).

(140 * 5x)/100 , (150 * 7x)/100 and ( 175 * 8x )/100

7x, (21/2)x and 14x.

The required ratio = 7x : (21/2)x : 14x

14x : 21x : 28x

2 : 3 : 4.

- 4. Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit’s new salary?

(a) 17000

(b) 20000

(c) 25000

**(d) 38000**

(e) None of these

Explanation:

Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.

Then, 2x + 4000 = 40

3x + 4000 57

57(2x + 4000) = 40(3x + 4000)

6x = 68,000

3x = 34,000

Sumit’s present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.

5. The maximum marks per paper in 3 subjects in Mathematics , Physics and Chemistry are set in the ratio 1 : 2 : 3 respectively. Giri obtained 40% in Mathematics, 60% in Physics and 35% in Chemistry papers. What is the overall percentage of mark that he secured?

**(a) 44**

(b) 32

(c) 50

(d) 60

(e) None of these

Explanation:

40*1/100 : 60*2/100 : 35*3/100 = 0.4:1.2:1.05

Overall % =100* [0.4+1.2+1.05]/1+2+3 = 265/6 = 44.16 = 44%

- Between two stations, the first, second and third class fares are in the ratio 9 : 7 : 2. The number of passengers travelling in a day are in the ratio 5 : 3 : 2, respectively, in the above classes. If the sale of tickets generated revenue of Rs. 98,000 that day and if 200 passengers travelled by third class, what was the fare for a first class ticket?

(a) Rs. 84

(b) Rs. 92

(c) Rs. 106

**(d) Rs. 126**

(e) Rs. 116

Explanation:

Ratio of number of passengers is 5 : 3 : 2

If 200 passengers travelled by third class,

500 must have travelled by first class

Sum of ratio of amount collected

= (5 × 9 + 3 × 7 + 2 × 2) = 45 + 21 + 4 = 70

Amount collected from 1st class

= (45/70) x 98000 = Rs. 63,000

Fare for the first class

= Rs. (36000/500) = Rs. 126

- If 378 coins consist of Rs. 1, 50 paise and 25 paise coins, whose values are in the ratio of 13 : 11 : 7, the number of 50 paise coins will be

**(a) 132**

(b) 128

(c) 136

(d) 133

(e) None of these

Explanation:

- A certain product C is made of two ingredients A and B in the proportion of 2: 5. The price of A is three times that of B. The overall cost of C is Rs. 5.20 per kg including labour charges of 80 paisa per kg. Find the cost of B per kg?

(a) Rs. 8.40

(b) Rs. 4.20

(c) Rs. 4.80

**(d) Rs. 2.80**

(e) None of these

Explanation:

- A factory employs skilled workers, unskilled workers and clerks in the proportion 8:5:1 and the wage of a skilled worker, an unskilled worker and a clerk are in the ratio 5:2:3. When 20 unskilled workers are employed, the total daily wages of all amount to Rs. 3180. Find the daily wages paid to each category of employees.

(a) 2100, 800,280

(b) 2400, 480, 300

(c) 2400, 600, 180

(d) 2200, 560, 420

(e) None of these

Explanation:

- The cost of a bat increased by 10 per cent and the cost of a ball increased by 18 per cent. Before the price rise, the ratio of the cost of the bat to the cost of the ball was 9:2. If the cost of 12 bats and 54 balls before the price rise was Rs. C, what is their cost (in Rs.) now?

(a) 1.12 C

(b) 1.13 C

**(c) 1.14 C**

(d) 1.15 C

(e) None of these

Explanation:

- From a number of mangoes, a man sells half the number of existing mangoes plus 1 to the first customer, then sells one-third of the remaining number of mangoes plus 1 to the second customer, then one-fourth of the remaining number of mangoes plus 1 to the third customer and one-fifth of the remaining number of mangoes plus 1 to the fourth customer. He then finds that he does not have any mango left. How many mangoes did he have originally?

(a) 12

**(b) 14**

(c) 15

(d) 13

(e) None of these

Explanation:

- The incomes of A, B and C are in the ratio 7:9:12 and their spendings 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

Explanation:

- On Republic Day, sweets were to be equally distributed among 450 children. But on that particular day, 150 children remained absent. Thus, each child got 3 sweets extra. How many sweets did each child get?

(a) 6

(b) 12

**(c) 9**

(d) Cannot be determined

(e) None of these

Explanation:

** **

- Mr. Pandit owned 950 gold coins all of which he distributed amongst his three daughters Lalita, Amita and Neela. Lalita gave 25 gold coins to her husband, Amita donated 15 gold coins and Neeta made jewellery out of 30 gold coins. The new respective ratio of the coins left with them was 20:73:83. How many gold coins did Amita receive from Mr. Pandit?

**(a) 380**

(b) 415

(c) 400

(d) 350

(e) None of these

Explanation:

- The number of candidates writing three different entrance exams is in the ratio 4:5:6. There is a proposal to increase these numbers of candidates by 40%, 60% and 85% respectively. What will be the ratio of increased numbers?

(a) 14:15:16

(b) 12:15:19

(c)13:19:21

**(d) 11:14:17**

(e) None of these

Explanation:

Given ratio of number of candidates is 4:5:6

Let the number of candidates for 3 exams be 4k, 5k and 6k respectively.

After increasing, number of candidates become (140% of 4k), (160% of 5k) & (185% of 6k)

That is, (140x4k)/100, (160x5k)/100 and (185x6k)/100

= 56k/10, 80k/10 and 111k/10

Now, the required new ratio = 56k/100 : 80k/10 : 111k/10

= 56 : 80 : 111

Hence the answer is option d.

- Published in RATIO AND PROPORTION