Ratio and Proportion
Q31. If 25% of P = 0.30 of Q = 1/3 of R, then P : Q : R is
(a) 12 : 100 : 9
(b) 14 : 110 : 9
(c) 15 : 120 : 9
(d) 16 : 130 : 9
Answer: (a) 12 : 100 : 9
25% of P = 0.30 of Q = 1/3 of R
⇒ | 25 | X P = 0.30 X Q = | 1 | X R |
100 | 3 |
⇒ | P | = | 3Q | = | R | = k (let) |
4 | 100 | 3 |
∴ P/4 = k 3Q/100 = k R/3 = k
⇒ P = 4k ⇒ Q = (100/3) k ⇒ R = 3k
∴ P : Q : R = 4k : (100/3) k : 3k = 12 : 100 : 9
Q32. The mean proportional of 234 and 104 is
(a) 146
(b) 152
(c) 157
(d) 163
Answer: (a) 146
Mean Proportional = √234 X 104
=√13 X 9 X 2 X 2 X 13 X 14
=√13 X 3 X 3 X 2 X 2 X 13 X 2 X 2
= 13 X 3 X 2 X 2 = 146
Q33. If 0.36 : x :: 3 : 5 then x = ?
(a) 0.4
(b) 0.6
(c) 0.7
(d) 0.9
Answer: (b) 0.6
0.36 : x :: 3 : 5
⇒ | 0.36 | = | 3 |
x | 5 |
⇒ 3x = 0.36 X 5
⇒ x = (0.36 X 5)/3 = 0.12 X 5 = 0.6
Q34. If x2 varies directly as y3 and when x = 5, y = 2 then
(a) 5x2 = 21y2
(b) 6x2 = 23y3
(c) 7x2 = 24y2
(d) 8x2 = 25y3
Answer: (d) 8x2 = 25y3
x2 α y3
⇒ x2 = ky3
⇒ 52 = k . 23
⇒ 25 = 8k
⇒ k = 25/8
∴ x2 = 25/8 y3
⇒ 8x2 = 25y3
Q35. If the angles of a triangle are in the ratio 3 : 4 : 5, the smallest one is
(a) 380
(b) 410
(c) 450
(d) 490
Answer: (c) 450
Let, the angles are 3x, 4x and 5x respectively
A/Q 3x + 4x + 5x = 1800
⇒ 12x = 1800
⇒ x = 150
∴ Smallest angle = 3 X 150 = 450
Q36. The ratio of a man's age to his son's age is 5 : 1. The product of their ages is 180. The ratio of their ages after 6 years will be
(a) 3 : 1
(b) 5 : 2
(c) 5 : 3
(d) 6 : 1
Answer: (a) 3 : 1
Let, the present ages be 5x, x year
A/Q 5x X x = 180
⇒ 5x2 = 180
⇒ x2 = 36
⇒ x = 6
∴ Man's present age = 5 X 6 = 30 y
Son's present age = 6 y
After 6 years, Ratio of Man's age : Son's age = 30 + 6 : 6 + 6 = 36/12 = 3 : 1
Q37. Rs. 2150 are divided among P, Q and R is such a way that the share of P is 2/5 of the combined share of Q and R. Thus P gets
(a) Rs. 500
(b) Rs. 550
(c) Rs. 600
(d) Rs. 750
Answer: (c) Rs. 600
P = 2/5 (Q + R)
⇒ p : (Q + R) = 2 : 5
∴ P's shave = | 2 | X 2100 = Rs. | 2 | X 2100 =Rs. 600 |
2 + 5 | 7 |
Q38. If x inversly proportional to y and for x = 2 y = 1/6, if x = 3 then y = ?
(a) 4
(b) 6
(c) 8
(d) 9
Answer: (a) 4
X α 1/y
⇒ x = k/y
⇒ 2 = k. (1/6)
⇒ k = 2 X 6 = 12
Now x = k. 1/y
⇒ 3 = 12 . (1/y)
⇒ 3y = 12
⇒ y = 4
Q39. If m is proportional to n and n = 10 when m = 3, then what is the value of n when m = 6 ?
(a) 13
(b) 18
(c) 20
(d) 23
Answer: (c) 20
Given m α n
⇒ m = kn
⇒ 3 = k.10
⇒ k = 3/10
Now m = kn
⇒ 6 = (3/10). n
⇒ n = 20
Q40. Rs. 2600 are divided among A, B, C and D in such a way that
A's share | = | B's share | = | C's share | = | 2 |
B's share | C's share | D's share | 3 |
What is B's share ?
(a) 405
(b) 430
(c) 480
(d) 510
Answer: (c) 480
A/B = 2/3 B/C = 2/3 C/D = 2/3
⇒ A = 2B/3 ⇒ B = 2C/3 ⇒ C = 2D/3
Here A = | 2B | = | 2 X (2C/3) | = | 4C | = | 4.(2D/3) | = | 8D |
3 | 3 | 9 | 9 | 27 |
Here B = | 2C | = | 2 X (20/3) | = | 4D |
3 | 3 | 9 |
Now A : B : C : D = | 8D | : | 4D | : | 2D | : D |
27 | 9 | 3 |
= 8 : 12 : 18 : 27
∴ B's share = Rs. | 12 | X 2600 = Rs. | 12 | X 2600 = Rs. 12 X 40 = Rs. 480 |
8 + 12 + 18 + 27 | 65 |
Practice Test Exam