Question

What is the value of \[10\] percent of \[y\] ?
(1) \[5\] percent of \[y\] is \[60\]
(2) \[y\] is \[80\] percent of \[1500\]
(a) Statement I alone is sufficient to answer the problem.
(b) Statement II alone is sufficient to answer the problem.
(c) Statement I and II both are needed.
(d) Either of the statements I or II both is sufficient.
(e) Statement I and II both are not sufficient.

Answer 1

Hint: In this question, we are asked to determine the value of \[10\] percent of \[y\] .To solve this question, we will solve both the given statements in the question individually using the concept of percentage i.e., \[x\% {\text{ }}of{\text{ }}y = \dfrac{x}{{100}} \times y\] and check whether the given statements are sufficient or not and then with the help of options we will check which option is the correct option.

Complete step-by-step answer:
In the question, we are asked to determine the value of \[10\] percent of \[y\]
Now, we know that \[x\% {\text{ }}of{\text{ }}y = \dfrac{x}{{100}} \times y\]
So, putting \[10\] percent of \[y\] into a mathematical expression, we can write
\[10\] percent of \[y\] equals to \[\dfrac{{10}}{{100}} \times y\]
\[ \Rightarrow 0.1y{\text{ }} - - - \left( 1 \right)\]
Now, we will solve both the given statements separately
Statement I: \[5\] percent of \[y\] is \[60\]
Now using \[x\% {\text{ }}of{\text{ }}y = \dfrac{x}{{100}} \times y\]
We can create the following information from statement I i.e.,
\[\dfrac{5}{{100}} \times y = 60\]
\[ \Rightarrow 0.05 \times y = 60\]
On dividing both sides by \[0.05\] we get,
\[y = \dfrac{{60}}{{0.05}}\]
\[ \Rightarrow y = \dfrac{{60}}{5} \times 100\]
On solving we get
\[ \Rightarrow y = 1200\]
Therefore, from equation \[\left( 1 \right)\] we get
\[0.1y = 0.1 \times 1200 = 120\]
Hence, \[10\] percent of \[y\] equals to \[120\]
which means we can answer the question with certainty; hence statement I is sufficient.
From above calculation, if we see from the options, we can eliminate the options (b), (c) and (e).
Now we will solve the statement II
Statement II: \[y\] is \[80\] percent of \[1500\]
Now using \[x\% {\text{ }}of{\text{ }}y = \dfrac{x}{{100}} \times y\]
We can create the following information from statement II i.e.,
\[y = \dfrac{{80}}{{100}} \times 1500\]
\[ \Rightarrow y = 0.8 \times 1500\]
On multiplying we get,
\[y = 1200\]
Therefore, from equation \[\left( 1 \right)\] we get
\[0.1y = 0.1 \times 1200 = 120\]
Hence, \[10\] percent of \[y\] equals to \[120\]
which means we can answer the question with certainty; hence statement II is sufficient.
Hence, from the above calculations we conclude that either of the statements I or II both is sufficient to find the value of \[10\] percent of \[y\]
So, we can eliminate option (a) as well
So, the correct answer is “Option D”.

Note: While solving these types of questions, do not answer directly after solving the first statement. Always solve all the given statements because sometimes the solution of the first statement alone may not give us the correct answer. Like in this question, if we solve only the first statement and answer accordingly, then our answer will be option (a) but that was correct.
Note that there is also a direct way to find the value of \[10\] percent of \[y\] from the statement I i.e.,
Statement I states that \[5\] percent of \[y\] is \[60\]
So, we can directly say that \[10\] percent of \[y\] will be \[120\] .There is no need to solve it.