# Ratio and Proportion ( 6 to 10 )

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Ratio and Proportion ( 6 to 10 ):

# APTITUDE QUESTIONS (RATIO AND PROPORTION):

6. If (a + b) : (b + c) : (c + a) = 6 : 7 :8 and (a + b + c) = 14, then the value of c is:

A)    6

B)    9

C)    10

D)    12

E)    None of these

Explanation:

Let (a + b) = 6k, (b + c) = 7k and (c + a) = 8k.
Then, 2 (a + b + c) = 21k <=> 2 * 14 = 21k <=> k = 28/21 = 4/3
∴ (a + b) = (6 * 4/3) = 8 => c = (a + b +c) – (a + b) = (14 – 8) = 6

7. If Rs.782 be divided into three parts proportional to 1/2 : 2/3 : 3/4, then the first part is:

A)    Rs. 182

B)    Rs. 190

C)    Rs. 196

D)    Rs. 204

E)    None of these

Explanation:

Ratio given = 7 : 5 : 3 : 4, sum of ratio terms = 19.
∴ 1st part = Rs. (782 * 6/23) = Rs.204

8. Two numbers are in the ratio 3 : 5. If 6 is subtracted from each, the new numbers are in the ratio 12 : 22. The smaller number is:

A)    27

B)    30

C)    49

D)    55

E)    None of these

Explanation:

Let the numbers be 3x and 5x. Then, (3x-6)/(5x-6)=12/22 <=> 22(3x – 6) = 12(5x – 6)
                                                                                                 <=> 6x = 60  x = 10
∴ The smaller number = (3 * 10) = 30

9. Rs. 968 were divided among A, B, C so that A : B = 5 : 4 and B : C = 9 : 10. Then, C gets:

A)    Rs. 320

B)    Rs. 400

C)    Rs. 450

D)    Rs. 475

E)    None of these

Explanation:

A : B = 5 : 4, B : C = 9 : 10 = (9 * 4/9) : (10 * 4/9) = 4 : 40/9
∴ A : B : C = 5 : 4 : 40/9 = 45 : 36 : 40
Sum of ratio = 45 + 36 + 40 = 121
∴ C’ share = Rs. (968 * 40/121) = Rs. 320

10. In a bag there are coins of 25p, 10p and 5p in the ratio of 1: 2 : 3. If there are Rs.12 in all, how many 5p coins are there?

A)    60

B)    80

C)    100

D)    50

E)    None of these

Explanation:

Let us consider 25p, 10p and 5p coins be x, 2x and 3x respectively.
Then, sum of their values = Rs. (25x/100 + (10*2x)/100 + (5 * 3x)/100) = Rs.60x/100
∴ 60x/100 = 12 <=> x = (12 * 100)/60 = 20
Hence, the number of 5p coins = (3 * 20) = 60