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- Total Questions 20
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1. If p, q, r, s are proportional, then (p – q) (p – r)/p
=

Correct Answers :

[B]

Explanation :

Assume a set of values for p, q, r, s such that they
are proportional i.e. p/q = r/s. Suppose we take p:q, as 1:4 and r:s as 3:12 we get the given expression:

(p – q)(p – r)/p = – 3 x – 2/1 = 6. This value is also
given by p + s – q – r and hence option (b) is correct.

2. What number must be added in each term of the
fraction 7/31 so that it may become 5 : 17?

Correct Answers :

[D]

Explanation :

Thus option (d) is correct.

3. If x varies inversely as y^{3} – 1 and is equal to 3 when
y = 2, find x when

y = 4.

y = 4.

Correct Answers :

[B]

Explanation :

x = k/(y^{3} – 1). This gives k = 3 x 7 = 21. When, y = 4,

the equation becomes x = 21/(43 – 1) = 21/63 = 1/3.

4. If *x* varies as *y*, and *y* = 4 when *x* = 12, find *x* when
*y* = 15.

Correct Answers :

[A]

Explanation :

*x* = *k**y* → 12 = 4k → k = 3 Hence, *x* = 3 X *y* When, *y* = 15, *x* = 3 X 15 = 45.

5. X varies jointly as Y and Z; and X = 6 when Y = 3,
Z = 2; find X when Y = 5,

Z = 7.

Z = 7.

Correct Answers :

[B]

Explanation :

X = K x Y x Z → It is known that when X = 6, Y = 3 and Z = 2. Thus we get 6 = 6K → K = 1.

Thus, our relationship between X, Y and Z becomes X = Y x Z. Thus, when Y = 5 and Z = 7 we get X = 35.

6. If x varies as y directly, and as z inversely, and
x = 12 when y = 3; find z when x = 4,

y = 5.

y = 5.

Correct Answers :

[D]

Explanation :

x = ky/z

We cannot determine the value of k from the given
information and hence cannot answer the question.

7. Divide ₹1400 into three parts in such a way that half
of the first part, one-fourth of the second part and
one-eighth of the third part are equal.

Correct Answers :

[B]

Explanation :

Solve this question using options. 1/2 of the first part should equal 1/4th of the second part and 1/8th of the third part. Only, option (b) satisfies these conditions thus this option is correct.

8. Divide ₹5000 among A, B, C and D so that A and
B together get 3/7^{th} of what C and D get together, C gets 1.5 times of what B gets and D gets 4/3 times
as much as C. Now the value of what B gets is

Correct Answers :

[B]

Explanation :

9. If each fraction is equal to

Correct Answers :

[B]

Explanation :

The given condition has p, q and r symmetrically placed. Thus, if we use p = q = r = 1 (say) we get each fraction as 1/2.

10. If 3x^{2} + 3y^{2} = 10xy, what is the ratio of x to y?

Correct Answers :

[C]

Explanation :

Solve using options. It is clear that a ratio of x:y as 1: 3 fits the equation.

11. If p : q = r : s, then the value of (p^{2} + q^{2})/(r^{2} + s^{2}) is

Correct Answers :

[D]

Explanation :

Let p = 1, q = 2, r = 3, s = 6
1 : 2 = 3 : 6 So, (p^{2} + q^{2})/(r^{2} + s^{2}) = 5/45 = 1/9.

From the given options, only pq/rs gives us this
value.

12. If p, q, r, s are in continued proportion then what is the value of x?

Correct Answers :

[B]

Explanation :

Experimentally if you were to take the value of p,
q, r, and s as 1 : 2 : 4 : 8, you get the value of the
expression as 3.5. If you try other values for p, q,
r and s experimentally you can see that while you
can approach 3, you cannot get below that.

For instance,
1 : 1.1 : : 1.21 : 1.331 Gives us: – 0.331/ – 0.11 which is slightly greater
than 3.

13. If 3 examiners can examine a certain number of
answer books in 10 days by working 4 hours a day,
for how many hours a day would 4 examiners have
to work in order to examine thrice the number of
answer books in 30 days?

Correct Answers :

[A]

Explanation :

3 X 10 X 4 = 120 man-hours are required for ‘x’ no. of answer sheets. So, for ‘3x’ answer sheets we would require 360 man-hours = 4 X 30 X n → n = 3 Hours a day.

14. In a mixture of 60 litres, the ratio of milk and water is
2 : 3. How much water must be added to this mixture so that the ratio of milk and water becomes 1 : 2?

Correct Answers :

[B]

Explanation :

In 60 liters, milk = 24 and water = 36. We want to create 1 : 2 milk to water mixture, for this we would need: 24 liters milk and 48 liters water. (Since milk is not increasing). Thus, we need to add 12 liters of water.

15. If *P* varies as *R*, and *Q* varies as *R*, then which of
the following is false:

Correct Answers :

[B]

Explanation :

Option (b) is not true.

16. If three numbers are in the ratio of 1 : 3 : 5 and half
the sum is 9, then the ratio of cubes of the numbers is:

Correct Answers :

[C]

Explanation :

1 : 3 : 5 → x, 3x and 5x add up to 18. So the numbers are: 2, 6 and 10. Ratio of cubes = 8 : 216 : 1000 = 1: 27: 125. />

17. The ratio between two numbers is 7 : 11 and their
LCM is 154. The first number is:

Correct Answers :

[A]

Explanation :

The numbers would be 7x and 11x and their LCM would be 77x. This gives us the values as 14 and 22. The first number is 14.

18. *P* and *Q* are two alloys of aluminum and brass prepared
by mixing metals in proportions 7: 2 and 7: 11, respectively. If equal quantities of the two alloys are
melted to form a third alloy *R*, the proportion of aluminum and brass in *R* will be:

Correct Answers :

[C]

Explanation :

Since equal quantities are being mixed, assume that
both alloys have 18 kgs (18 being a number which is the LCM of 9 and 18).

The third alloy will get, 14 kg of aluminum from the
first alloy and 7 kg of aluminum from the second
alloy. Hence, the required ratio: 21:15 = 7:5

19. If 10 men working 6 hours a day can do a piece of
work in 15 days, in how many days will 20 men working 14 hours a day do the same work?

Correct Answers :

[A]

Explanation :

The total number of man-days-hours required = 10 X 6 X 15 = 900 20 X 14 X number of days = 900 → number of days = 900/280 = 3.21 days

20. The incomes of *P* and *Q* are in the ratio 1: 2 and
their expenditures are in the ratio 1: 3. If each saves ₹500, then, P’s income can be:

Correct Answers :

[A]

Explanation :

Solve using options. Option (a) fits the situation as
if you take P’s income as ₹1000, Q’s income will become ₹2,000 and if they each save ₹500, their
expenditures would be ₹500 and ₹1500 respectively.

This gives the required 1:3 ratio.

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