Division of a given quantity in a given ratio

Question 1

On Snigdha's birthday, her father brought a flower bouquet that contain 18 flowers in all. If the ratio of red flowers to yellow is 1 : 2. Find their number.

Solution: Ratio of red flowers to yellow flowers = 1 :

Total parts = 1 + 2 = parts

Total number of flowers = flowers

3 parts = 18 flowers

Each part = 183 = flowers

Red flowers = 1 part = 1 × 6 flowers = flowers

Yellow flowers = 2 parts = 2 × 6 flowers = flowers.

Question 2

A goldsmith mixes gold and copper in the ratio 7:2 to prepare an ornament. If the ornament weighs 45gms, find the weight of gold and copper in it.

Solution:

Ratio of gold and copper = : 2

Sum of the ratio terms = 7 + 2 =

Weight of 9 parts = gm

Weight of Each part = 45 ÷ 9 = gm

Part of gold weighs = 7 parts × 5 gm = gm

Part of copper weighs = 2 parts × 5 gm = gm

Question 3

Line segment AB is divided into five equal parts.

(i) In what ratio does X divide line segment AB?

(ii) If the length of the line segment AB is 15 cm, find the length of the line segments AX and XB.

Solution:

(i) X divides AB in the ratio 3 :

(ii) Total parts = 3 + 2 = parts

Length of line segment AB = cm

Length of 5 parts = 15 cm

Length of each part = 15 ÷ 5 = cm

Length of line segment AX = 3 parts × 3 cm = cm

Length of line segment XB = 2 parts × 3 cm = cm

Question 4

Hari and Teja won a Lottery, which they agreed to share in the ratio of 5:3. If Teja received ₹150, how much did Hari receive? Also find the total amount.

Solution:

Ratio of Teja's amount to Hari's amount is = :

Teja has 3 parts, if 3 parts =

1 part = 150 ÷ 3 =

and 5 parts = 50 × 5 =

Hari will receive ₹250 and the total amount is = 250 + 150 = ₹