Sample questions to master ratio and proportion topic

Hyderabad: This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment tests. Ram and Shyam were carrying some money such that their money was in the ratio 3:8. A […]

Hyderabad: This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment tests.

Ram and Shyam were carrying some money such that their money was in the ratio 3:8. A friend gives each of them Rs 5 and their money is now in the ratio 2:5. Which is the smaller money of the two?
a. 45
b. 64
c. 105
d. 120
Ans: a

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Solution:
Ratio of original money numbers = 3:8
Common factor helps in finding actual values easily
So, take ‘M’ as common factor.
∴ Original numbers will be 3M and 8M
Adding 5 to them, we get (3M 5) and (8M 5)
∴ 3M 5 / 8M 5 = 2/5 —————–>; (Ratio of new numbers is 2:5)
∴ 15M 25 = 16M 10
∴ M = 15
Smaller money value is 3M = 3 x 15 = 45

Q. A child has three different kinds of chocolates costing Rs 2, Rs 5, and Rs 10. He spends total Rs 120 on the chocolates. What is the minimum possible number of chocolates he can buy, if there must be at least one chocolate of each kind?
a. 22
b. 19
c. 17
d. 15
Ans: c

Solution:
The minimum number of chocolates is possible when he purchases maximum number of costliest chocolates.
Thus, 2 x 5 5 x 2 = Rs 20
Now, Rs 100 must be spend on 10 chocolates as 100 = 10 x 10.
Thus minimum number of chocolates = 5 2 10 = 17

Q. Vinod has Rs 20. He bought Rs 1, Rs 2, Rs 5 stamps. They are different in numbers by the reason of no change. The shop keeper gives 3 Rs 1 stamps, so how many stamps does Vinod have?
a. 10
b. 18
c. 12
d. 15
Ans: a

Solution:
Given total rupees = Rs 20
No. of Rs 1 stamps = 3
Now, remaining money = Rs 17
With that he buys only Rs 2 and Rs 5 rupee stamps
Let number of Rs 5 stamps = K
Let number of Rs 2 stamps = L
5K 2L = 17
K = 3, L = 1 (possible)
L = 6, K = 1 (possible)
=>; But given that they are different in number so, K is not equal to 3
Rs 1 stamps = 3
Rs 2 stamps = 6
Rs 5 stamps = 1
Total number of stamps = 10

Q. For any two numbers m, n; (m n): (m-n): mn = 7: 1: 60. Find the value of 1/m: 1/n.
a. 4:3
b. 8:7
c. 3:4
d. 7:8
Ans: c

Solution:
m nm − n = 7xx ⇒ mn = 4x3xm nm-n = 7xx ⇒ mn = 4x3x
Again, mn = 12 x 2mn = 12×2
and mn = 60x
so, 60x = 12×2 ⇒ x = 560x = 12×2 ⇒ x = 5
=>; m = 20 and n = 15
Hence, 1/m:1/n = 120:115 = 3:4

To be continued…

M. Venkat
Director
MVK Publications
Dilsukhnagar
7671002120