Q. 24.4( 12 Votes )

# Two angles are in the ratio 1 : 2. On increasing the smaller angle by 6° and decreasing the larger angle by 6°, the ratio changed to 2 : 3. What were the original angles?

Answer :

Let the two angles be x and 2x

Increasing smaller by 6° and decreasing the larger by 6°, the ratio changes to 2: 3

⇒

⇒ 3×(x + 6) = 2×(2x – 6)

⇒ 3x + 18 = 4x – 12

⇒ 4x – 3x = 18 + 12

⇒ x = 30

Original angles are 30° and 2x = 2× 30 = 60°

∴ Original angles are 30° and 60°

Rate this question :

There are four right triangles, the ratio of perpendicular sides being 3 : 4 in each. Once more fact about each is given below. Find the lengths of the sides of each triangle.

The difference in the lengths of the perpendicular sides is 24 meters.

Kerala Board Mathematics Part IIThe breadth and length of two rectangles are in the ratio 2 : 3. In another rectangle, whose breadth is 1 centimetres less and length is 3 centimetres less than those of the first, this is 3 : 4. Calculate the breadth and length of both rectangles.

Kerala Board Mathematics Part IIIn the above problem, what if the capacities of the bottles are in the ratio 4 : 7?

Kerala Board Mathematics Part IIThe capacities of two bottles are in the ratio 3 : 4. The smaller bottle was filled twice and the larger bottle was filled and emptied into a vessel. Twice the smaller and half the larger was emptied into another. What is the ratio of the quantities of water in the two vessels?

Kerala Board Mathematics Part IITwo angles are in the ratio 1 : 2. On increasing the smaller angle by 6° and decreasing the larger angle by 6°, the ratio changed to 2 : 3. What were the original angles?

Kerala Board Mathematics Part IITwo quantities are in the ratio 3 : 5.

(i) If the smaller alone is made four times the original, what would the ratio be?

(ii) If the smaller is doubled and the larger is halved, what would the ratio be?

Kerala Board Mathematics Part IIThe sides of a rectangle are in the ratio 4 : 5.

By what fraction should the longer side be decreased to make it a square?

Kerala Board Mathematics Part IIThere are four right triangles, the ratio of perpendicular sides being 3 : 4 in each. Once more fact about each is given below. Find the lengths of the sides of each triangle.

The area is 24 square metres.

Kerala Board Mathematics Part II