The sum of the three consecutive odd numbers is 285. What is the ratio of the smallest and largest numbers respectively?
The sum of the three consecutive odd numbers is 285. What is the ratio of the smallest and largest numbers respectively?
The sum of the three consecutive odd numbers is 285. What is the ratio of the smallest and largest numbers respectively?
Nithin ? undefined
Correct answer is: 93 : 97
Explanation:
x + x + 2 + x + 4 = 285
\(\implies 3x = 285 - 6 = 279\)
\(\implies x = = 93\)
Therefore, Required ratio = 93 : 97
A camel pursues an elephant and takes 5 leaps for every 7 leaps of the elephant, but 5 leaps of elephant are equal to 3 leaps of camel. What is the ratio of speed of camel and elephant?
Nithin ? undefined
Correct answer is: 25 : 21
Explanation:
Required ratio = \(\frac{5}{3} : \frac{7}{5}\)
\(= \frac{5}{3} \times 15 : \frac{7}{5} \times 15 = 25 : 21\)
A shopkeper placed on display some shirts each with a marked price. He then posted a board $\frac{1}{4}$ off on shirts". If the cost of a shirt was $\frac{2}{3}$ of the price at which it was actually sold, the ratio of cost and marked price 01' shirt was
Nithin ? undefined
Correct answer is: 1 : 2
Explanation:
Let. S.P. of shirt = x
\(\text{C.P = }\frac{2x}{3}\)
Therefore, Marked price
\(= \frac{4}{3} \times x = \frac{4x}{3}\)
Therefore, Required ratio = \(\frac{2x}{3} : \frac{4x}{3} = 1 : 2\)
The price of a diamond is proportional to the square of its mass, which is measured in carats. A 6 carat diamond was broken into two parts and total price of the two pieces is $\frac{5}{8}$ th of the price of original diamond. The masses (in carat) of two pieces are
Nithin ? undefined
Correct answer is: 4.5 and 1.5
Explanation:
Actual price of diamond = \( k \times 6^{2}\)
= 36k where k is constant of proportionately.
New price of diamond\(=kx^{2}_{1} + kx^{2}_{2}\)
\(= 36k \times \frac{5}{8} = k \left(x^{2}_{1} + x^{2}_{2}\right)\)
\(= \frac{45}{2} = x^{2}_{1}+x^{2}_{2}\)
\(= 22.5 = x^{2}_{1}+x^{2}_{2}\)
\(= \left(4.5\right)^{2}+ \left(1.5\right)^{2} = x^{2}_{1}+x^{2}_{2}\)
Abhijit invested in three schemes A, B and C the amounts in the ratio of 2 : 3 : 4 respectively. If the schemes offered interest @ 20 p.c.p.a. 16 p.c.p.a. and 15 p. c.p. a. respectively, what will be the respective ratio of the amounts after one year ?
Nithin ? undefined
Correct answer is: None of these
Explanation:
Let the amount invested in schemes A, B aand C in Rs. respectively be 2x, 3x and 4x
Amount after 1 year in scheme :
\(A = \frac{120}{100} \times 2x = 2.4 x\)
\(B = \frac{116}{100} \times 3x = 3.48x\)
\(C = \frac{115}{100}\times 4x =4.6x\)
\(\implies \text{Required ratio =} 2.4: 3.48:4.6\)
\(= 60:87:115\)
The angles of a quadrilateral are in ratio of 3 : 5 : 9 : 7. The second largest angle of the quadrilateral is equal to the largest angle of a triangle. One of the angles of the triangle is $25^∘$. What is the value-of second largest angle of the triangle?
Nithin ? undefined
Correct answer is: \(50^o\)
Explanation:
Sum of ratios = 3 + 5 + 9 + 7 = 24
Second largest angle of quadrilateral = \(\frac{7}{24} \times 360 = 105 ^{\circ}\)
Largest angle of triangle
Therefore, Third angle of triangle = \(\frac{7}{24} \times 360 = 105 ^{\circ}\)\(=180 ^{\circ} - 105 ^{\circ} - 25 ^{\circ}\)
\(= 50^∘ = \text{second largest angle of triangle.}\)
The cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1:2:3:4. If the loss in total value of the diamond was the ₹ 70,000, what was the price of the original diamond?
Nithin ? undefined
Correct answer is: ₹ 1,00,000
Explanation:
\(Cost ∝ (weight)^2\)
Total weight of original diamond = 1k + 2k + 3k + 4k = 10k, where k is positive integer
Cost of original diamond = \((10k)^2\) = \(100k^2\)
Total cost of four broken pieces = \(k^2\)(1 + 4 + 9 + 16) = 30\(k^2\)
The value of broken pieces is 70,000 less than the original diamond.
Difference in cost = 70,000
\(100k^2 - 30k^2 = 70,000\)
\(70k^2 = 70,000\)
\(k^2 = 1,000\)
Cost of original diamond = \(100k^2 = 100 × 1,000\)
= 1,00,000