Practice Questions for Arithmetic - Ratio, Proportion & Variation

1. PE 2 - Ratio | Arithmetic - Ratio, Proportion & Variation

Divide Rs. 6270 among A, B and C so that A shall receive 3/7 of as much as B and C together and B shall receive 2/9 of as much as A and C together:

(a)
1881, 1240, 3149
(b)
1881, 1040, 3349
(c)
1881, 1250, 3139
(d)
1881, 1140, 3249

2. PE 2 - Ratio | Arithmetic - Ratio, Proportion & Variation

If $\frac{x}{a}$ = $\frac{y}{b}$ = $\frac{z}{c}$ , then $\frac{a x - b y}{(a + b) (x -y)}$ + $\frac{b y - c z}{(b + c) (y - z)}$ + $\frac{c z - a x}{(c + a) (z - x)}$ is equal to

(a)
2
(b)
3
(c)
1
(d)
0

3. PE 2 - Ratio | Arithmetic - Ratio, Proportion & Variation

If a/b = c/d = e/f, then the value of which of the following is equal to the value of $\frac{a^{3} + c^{3} + e^{3}}{b^{3} + d^{3} + f^{3}}$

(a)
1/2
(b)
$\frac{a + c + e}{b + d + f}$
(c)
$\frac{a c e}{b d f}$
(d)
None of these

4. PE 2 - Ratio | Arithmetic - Ratio, Proportion & Variation

Between two stations the first, second and third class fares were fixed in the ratio 8 : 6 : 3, but afterwards the first class fares were reduced by 1/6 and the second class by 1/12. In a year, number of first, second and third class passengers were respectively 9 : 12 : 26 and the money at the booking offices was Rs. 1088. How much was paid by the first class passengers?

(a)
10 × 2²
(b)
10 × 2³
(c)
10 × 2⁴
(d)
10 × 2⁵

5. PE 2 - Ratio | Arithmetic - Ratio, Proportion & Variation

There are two persons P and Q and P’s present age is less than Q’s present age. Which of the following will be the relation between cubes of the ratio of their ages after 4 years (M) and the ratio of their ages after 8 years (N)?

(a)
M < N
(b)
M = N
(c)
M > N
(d)
M ≤ N

6. PE 2 - Ratio | Arithmetic - Ratio, Proportion & Variation

The ratio of the present ages of a man and his wife is 6 : 5. Which of the following can’t be a possible ratio of their ages 10 years ago?

(a)
8 : 7
(b)
3 : 2
(c)
13 : 10
(d)
7 : 5

7. PE 2 - Ratio | Arithmetic - Ratio, Proportion & Variation

The reduction in speed of a locomotive engine is directly proportional to square root of no. of wagons attached to it. Speed of engine was 240 km/hr when no wagons were attached to it. When 49 wagons were attached the speed became 100 km/hr. Maximum how many wagons can be attached to engine such that engine keeps on moving?

(a)
145
(b)
144
(c)
143
(d)
147

8. PE 2 - Ratio | Arithmetic - Ratio, Proportion & Variation

A sick man’s will stipulated that if his pregnant wife gave birth to a boy, then she should get two-fifth of his property and the child should get the remaining three-fifth. On the other hand, if she gave birth to a girl child, then one-fourth should go to his wife and the remaining three-fourth to the child. The sick man died after a few weeks. His wife delivered twins, a boy and a girl. How much should the wife get if his net-worth is Rs. 1.32 crores.

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9. PE 2 - Ratio | Arithmetic - Ratio, Proportion & Variation

A certain sum is divided among A, B and C in a manner that for every rupee that A gets, B gets 50 paise and for every rupee that B gets, C gets 25 paise. If C’s share in the total sum is Rs. 520, then find the share of A (in Rs.).

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10. PE 2 - Ratio | Arithmetic - Ratio, Proportion & Variation

Three friends count the number of coins they have. They found that the ratio of the total number of coins of 25 p, 50 p and Re 1 is 2 : 3 : 5. They have 25 p coins in the ratio 1 : 2 : 3, 50 p coins in the ratio 2 : 3 : 4 and Re 1 coins in the ratio 4 : 5 : 6. Find the amount with the second person (in Rs.), if they have money only in the denomination of 25 p, 50 p and Re 1 and the total number of coins with them is 540.

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PE 2 - Ratio | Arithmetic - Ratio, Proportion & Variation

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