SSC CGL MATHS QUIZ-24

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Question 1:

The average age of 14 girls and  teacher's is 16 years. If teacher's age is excluded the average reduced by 1 . What is the teacher's age.

Question 2:

If a and b be two rational numbers, find the value of  b.

 $\frac{3+\sqrt{7}}{3-\sqrt{7}}=a+b \sqrt{7}$

Question 3:

A and B started a partnership business investing some amount in the ratio of $3: 2$. C joined them after 6 months with an amount equal to that of A. In what proportion should the profit at the end of the one year be distributed among A, B and C?

Question 4:

If $\frac{2 x}{5 x^{2}-7 x+5}=\frac{1}{3}$, then find the value of $x^{2}+\frac{1}{x^{2}}$.

Question 5:

After allowing a discount of 10% on the marked price of an article, it is sold for Rs.450 . Had the discount not been given, the profit would have been 25%. What is the 50% of the cost price (in Rs.) of the article?

Question 6:

600 grams of sugar solution has $40 \%$ of sugar in it, How much sugar should be added to make it $50 \%$ in the Solution?

Question 7:

A sum of money amounts to ₹ 1,113 in 9 years at $9.5 \%$ per annum simple interest. The amount invested initially was:

Question 8:

A cylindrical vessel of diameter $32 \mathrm{~cm}$ is partially filled with water. A solid metal sphere of radius $12 \mathrm{~cm}$ is dropped into it. How high will the water level in the vessel (in $\mathrm{cm}$) rise?

Question 9:

Two circles of radii $8 \mathrm{~cm}$ and $2 \mathrm{~cm}$ respectively touch each other externally at the point A. PQ is the direct common tangent of those two circles of centres $\mathrm{O}_{1}$ and $\mathrm{O}_{2}$ respectively. Then length of $\mathrm{PQ}$ is equal to:

Question 10:

If $\tan 45^{\circ}+\sec 60^{\circ}+\operatorname{cosec} 30^{\circ}=x$, then find the value of $x$