The sum of three numbers is 132. If the ratio of the first to the second is 2:5 and the ratio of the second to the third is 5:4, then the first number is:
24
Given: three numbers add up to 132, with first : second = 2 : 5 and second : third = 5 : 4.
The second number appears as 5 in both ratios, so they combine directly.
Therefore first : second : third = \(2 : 5 : 4\).
The total number of ratio parts is \(2 + 5 + 4 = 11\).
Each part equals \(\frac{132}{11} = 12\).
The first number corresponds to 2 parts: \(2 \times 12 = 24\).
Check: the numbers are 24, 60 and 48, whose sum is \(24 + 60 + 48 = 132\), as required.
Hence the first number is 24.
Similar Questions
If (x+y):(y+z):(z+x)=7:9:13 for positive reals x,y,z, find x:y:z?
The ratio of gold to copper in a bracelet is 4 : 7. If the price of copper is 1/10th the price of gold, find the cost of the bracelet if the cost of copper in the bracelet is 28000 rupees.
Three numbers are in a ratio 5 : 7: 9. If the difference between the largest and the smallest number is 20, find the middle number.
The profits of three partners are in the ratio 2 : 3 : 4. If their profits increase by 50%, 40%, and 30%, what is the new ratio of profits?
Two numbers are such that 30% of the first is equal to 45% of the second. What is the ratio of the first to the second?
The sum of three numbers A, B and C is given as 3500. If the ratio of A to B is 2:3 and the ratio of B to C is 4:5 then what is the value of B?
If a : b = 9 : 5, b : c = 4 : 11. Find a : c.
In a class, ratio of the boys to the girls is 5:3. If 20% of the boys and 40% of the girls fail an exam, what is the ratio of the number of boys who passed to the number of girls who passed?
A and B together have Rs. 9000. If \(\frac{4}{11}\) of A's amount is equal to \(\frac{3}{5}\) of B's amount, how much amount does A have?
Important Questions from Ratio and Proportion
In a mixture of 156 litres, the ratio of milk and water is 7 : 6. How much water should be added to make the ratio 14 : 13?
If the ratio of the first to second number is 3 : 4 and that of the second to the third number is 8 : 5, and sum of three numbers is 190 then the third number is:
The third proportional to 9 and 15 is:
The average age of 3 persons is 30 years.If their ages are in the ratio of 3 : 5 : 7 respectively, then the age of the eldest person is:
The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio of 8 : 5 : 2. If C spends 2000 and B saves ₹ 700, then A saves:
